ABAQUS/Standard is a powerful finite element program designed for general use in nonlinear problems. The paper touches only one aspect of usage of the software, namely a constitutive modelling of slightly compressible hyperelastic materials. It begins with a discussion of a well-known approach of describing slight compressibility in the context of the stored energy function. Basic equations of continuum mechanics are presented as well. The main part of the work concerns an implementation of one of the presented models. To this end, the UHYPER user subroutine is employed. Analytical formulas for a few simple, homogeneous deformation states are given which allow verifying numerical results. Finally, a couple demonstration examples with nonhomogeneous deformations are presented as an attempt at motivating applications in engineering.