This paper presents some analytical results and some test results for different mechanical problems, which are then simulated using finite element analysis with tetrahedral and hexahedral shaped elements. The comparison is done for linear static problems, modal analyses and nonlinear analyses involving large deflections, contact and plasticity. The advantages and disadvantages are shown using tetrahedral and hexahedral elements. We also present the limitations in operating and hardware systems when solving large finite element models by using quadratic tetrahedral elements. Some recommendations and general rules are given for finite element users in choosing the element shape.