Solving radiation shielding problems, i.e. deep penetration problems, is a challenging task from both computation time and resource aspects in field of nuclear engineering. This is mainly because of the complexity of the governing equation for neutral particle transport - Linear Boltzmann Equation (LBE). The LBE includes seven independent variables with presence of integral and differential operators. Moreover, the low successive rate of radiation shielding problem is also challenging for solving such problems. In this dissertation, the Detector Response Function (DRF) methodology is proposed and developed for real-time and accurate radiation shielding calculation. The real-time capability of solving radiation shielding problem is very important for: (1) Safety and monitoring of nuclear systems; (2) Nuclear non-proliferation; and (3) Sensitivity study and Uncertainty quantification. Traditionally, the difficulties of solving radiation problem are: (1) Very long computation time using Monte Carlo method; (2) Extremely large memory requirement for deterministic method; and (3) Re-calculations using hybrid method. Among all of them, the hybrid method, typically Monte Carlo + deterministic, is capable of solving radiation shielding problem more efficiently than either Monte Carlo or deterministic methods. However, none of the aforementioned methods are capable of performing "real-time" radiation shielding calculation. Literature survey reveals a number of investigation on improving or developing efficient methods for radiation shielding calculation. These methods can be categorized by: (1) Using variance reduction techniques to improve successive rate of Monte Carlo method; and (2) Developing numerical techniques to improve convergence rate and avoid unphysical behavior for deterministic method. These methods are considered clever and useful for the radiation transport community. However, real-time radiation shielding calculation capability is still missing although the aforementioned advanced methods are able to accelerate the calculation efficiency significantly. In addition, very few methods are "Physics-based" For example, the mean free path of neutrons are typically orders of magnitude smaller than a nuclear system, i.e. nuclear reactor. Each individual neutron will not travel too far before its history is terminated. This is called the "loosely coupled" nature of nuclear systems. In principle, a radiation shielding problem can be potentially decomposed into pieces and solved more efficient. In the DRF methodology, the DRF coefficients are pre-calculated with dependency of several parameters. These coefficients can be directly coupled with radiation source calculated from other code system, i.e. RAPID (Real-time Analysis for Particle transport and In-situ Detection) code system. With this arrangement, detector/dosimeter response can be calculated on the fly. Thus far, the DRF methodology has been incorporated into the RAPID code system, and applied on four different benchmark problems: (1) The GBC-32 Spent Nuclear Fuel (SNF) cask flooded with water with a $^3$He detector placed on the cask surface; (2) The VENUS-3 experimental Reactor Pressure Vessel (RPV) neutron fluence calculation benchmark problem; (3) RPV dosimetry using the Three-Mile Island Unit-1 (TMI-1) commercial reactor; and (4) A Dry storage SNF cask external dosimetry problem. The results show that dosimeter/detector response or dose value calculations using the DRF methodology are all within $2sigma$ relative statistical uncertainties of MCNP5 + CADIS (Consistent Adjoint Driven Importance Sampling) standard fixed-source calculation. The DRF methodology only requires order of seconds for the dosimeter/detector response or dose value calculations using 1 processor if the DRF coefficients are appropriately prepared. The DRF coefficients can be reused without re-calculations when a model configuration is changed. In contrast, the standard MCNP5 calculations typically require more than an hour using 8 processors, even using the CADIS methodology. The DRF methodology has enabled the capability of real-time radiation shielding calculation. The radiation transport community can be greatly benefited by the development of DRF methodology. Users can easily utilize the DRF methodology to perform parametric studies, sensitivity studies, and uncertainty quantifications. The DRF methodology can be applied on various radiation shielding problems, such as nuclear system monitoring and medical radiation facilities. The appropriate procedure of DRF methodology and necessary parameters on DRF coefficient dependency will be discussed in detail in this dissertation. / Doctor of Philosophy / Since the beginning of nuclear era, enormous amount of radiation applications have been proposed, developed, and applied in our daily life. The radiation is useful and beneficial when they are under control. However, there will be some "unwanted radiation" from these applications, which have to be shielded. For this, radiation shielding has become a very important task. To effectively shield the unwanted radiations, studying the thickness and design of the shields is important. Instead of directly performing experiments, computation is a more affordable and safer approach. The radiation shielding computation is typically an extremely difffficult task due to very limited "communication" between the radiation within the shield and detector outside the shield. In general, it is impractical to simulate the radiation shielding problems directly because the extremely expensive computation resources. Most of interactions of radiation are within the shield while we are only interested in how many of them penetrate through the shield. This is typically called "deep penetration" problems in the radiation transport community.