Residual stresses in rolled plates, used as raw material for the fabrication of aircraft components, arise from manufacturing processes such as rolling, casting, quenching, stretching, and thermal treatments. After each process, the rolled plate has a geometrically stable condition but with internal stresses. However, during part machining an unbalance in the distribution of residual stresses occurs, in special for aircraft components, due to the large amount of material removal throughout the process. This condition of instability leads to component distortions so that any corrective action affects the manufacturing lead-time and production costs. Part distortions are usually predicted by finite element analyses with linear tetrahedral meshes in which the residual stress profiles are applied as a constant value element-wise. In this work, both linear and quadratic solid meshes are employed to address this problem. For this purpose, a Python-based routine is implemented to apply the residual stress profile at the integration points of the elements. Then, finite element simulations of simple geometric configurations (plates and beams) under theoretical and real residual stress distributions are carried out. Performance and effectiveness of two different meshes—tetrahedral and hexahedral (brick-type)—are checked through comparison with results presented by classical plate and beam theories. A general good correlation for the deflections predicted by them is reached.