Uncertainty analysis is crucial to any thorough analysis of an engineering system. Traditional uncertainty analysis can be a tedious task involving numerous steps that can be error prone if conducted by hand. If conducted with the aid of a computer, these tasks can be computationally expensive. In either case, the process is quite rigid. If a parameter of the system is modified or the system configuration is changed, the entire uncertainty analysis process must be conducted again giving more opportunities for calculation errors or computation time. Modular uncertainty analysis provides a method to overcome all these obstacles of traditional uncertainty analysis. The modular technique is well suited for computation by a computer which makes the process somewhat automatic after the initial setup and computation errors are reduced. The modular technique implements matrix operations to conduct the analysis. This in turns makes the process more efficient than traditional methods because computers are well suited for matrix operations. Since the modular technique implements matrix operations, the method is adaptable to system parameter or configuration modifications. The modular technique also lends itself to quickly calculating other uncertainty analysis parameters such as the uncertainty magnification factor, and the uncertainty percent contribution. This dissertation will focuson the modular technique, the extension of the technique in the form the uncertainty magnification factor and uncertainty percent contribution, and the application of the modular technique to different type of energy systems. The modular technique is applied to an internal combustion engine with a bottoming organic Rankine cycle system, a combined heat and power system, and a heating, ventilation, and air conditioning system. The results show that the modular technique is well suited to evaluate complex engineering systems. The modular technique is also shown to perform well when system parameters or configurations are modified.