(eng): Many processes in mechanics and thermodynamics can be formulated as a minimization of a particular energy functional. The finite element method can be used for an approximation of such functionals in a finite-dimensional subspace. Consequently, the numerical minimization methods (such as quasi-Newton and trust region) can be used to find a minimum of the functional. Vectorization techniques used for the evaluation of the energy together with the assembly of discrete energy gradient and Hessian sparsity are crucial for evaluation times. A particular model simulating the deformation of a Neo-Hookean solid body is solved in this contribution by minimizing the corresponding energy functional. We implement both P1 and rectangular hp-finite elements and compare their efficiency with respect to degrees of freedom and evaluation times.