Modeling and simulation have played an essential role in understanding the effects of blast waves. However, a broad area of engineering problems, such as vehicle structures, buildings, bridges, or even the human body, can benefit by accurately predicting the response to blasts with little need for test or event data. This thesis reviews fundamental concepts of blast waves and explosives and discusses research in blast scaling. Blast scaling is a method that reduces the computational costs associated with modeling blasts by using empirical data and numerically calculating blast field parameters over time for various types and sizes of explosives. This computational efficiency is critical in studying blast waves' near and far-field effects. This thesis also reviews research to differentiate between free-air blasts and gun muzzle blasts and the progress of modeling the muzzle blast-structure interaction. The main focus of this thesis covers an investigation of different numerical and analytical solutions to a simple aerospace structure subjected to blast pressure. The thesis finally presents a tool that creates finite element loads utilizing muzzle blast scaling methods. This tool reduces modeling complexity and the need for multiple domains such as coupled computational fluid dynamics and finite element models by coupling blast scaling methods to a finite element model. / Master of Science / {Numerical integration methods have helped solve many complex problems in engineering and science due to their ability to solve non-linear equations that describe many phenomena. These methods are beneficial because of how well they lend to programming into a computer, and their impact has grown with the increases in computing power. In this thesis, ``modeling and simulation" refers to the characterization and prediction of an event's outcome through the use of computers and numerical techniques. Modeling and simulation play important roles in studying the effects of blast waves in many areas of engineering research such as aerospace, biomedical, naval, and civil. Their capability to predict the outcome of the interaction of a blast wave to vehicle structures, buildings, bridges, or even the human body while requiring limited experimental data has the chance to benefit a wide area of engineering problems. This thesis reviews fundamental concepts of blast waves, explosives, and research that has applied blast loading in modeling and simulation. This thesis describes the complexity of modeling an axially symmetric blast wave interaction by comparing the numerical and theoretical response blast loaded structure.