One of the key factors for obtaining accurate and reliable results using the Finite Element Method (FEM) is the dis-cretization of the domain. Traditionally, two main types of elements are used for three-dimensional mesh generation: tetrahedral and hexahedral elements. Tetrahedral meshes are automatically generated but standard displacement-based tetrahedral elements generally suffer from performance issues in terms of convergence rate and accuracy of the solution associated with volumetric and shear locking. Because of these distinct disadvantages, hexahedral meshes have been used up until now for the design of biomechanical models of the orofacial system in particular for medical applications. However, hexahedral meshing is very costly and labor intensive when the mesh must be handmade. The aim of the present contribution is to evaluate the performance of mixed-element meshes as an alternative to all-tetrahedral or all-hexahedral meshing for the analysis of problems involving nearly incompressible materials at large strains. The case study of a semi-confined compression experiment of an elastic cylindrical specimen was analyzed. The theoretical expression of deformation was derived from the literature. We observed that linear mixed-element meshes allowed results very close to those obtained using hexahe-dral ones. As a second experiment, we generated a mixed-element mesh of the tongue and analyze its simulated response to activation of the posterior Genioglossus muscle. Overall, our results show that mixed-element meshes can be used as computationally less demanding alternative to all-hexahedral meshes for the analysis of problems involving