In this article, the performance of two analytical methods known as the homotopy perturbation method (HPM) and Adomian decomposition method (ADM) on solving linear and nonlinear boundary value problems structural engineering and fluid mechanics are compared. In order to compare these mathematical models, various problems in inelastic and viscoelastic flows, deformation of beams, and plate deflection theory are chosen. In addition, the results of these two methods are compared with exact solutions to evaluate the precision and accuracy of these numerical methods.