In this talk, we focus on the modeling and simulation of large-strain (hyperelastic) elasticity problems, with particular application to the study of soft biological tissues. We also consider frictional contact between two hyperelastic bodies, with application to the deployment of a stent in an arterial tissue. For the numerical approximation, the key idea is to design a time integration scheme consistent with the energy of the system on the continuous level: that is, conserving energy in the frictionless contact case, and such that no numerical dissipation is introduced in the frictional and, possibly, viscosity cases. The numerical approximation of frictional contact is accomplished using a Primal–Dual Active Set method, without the need to introduce Lagrange multipliers. Numerical simulations are performed on academic and real-world scenarios; in particular, the latter concerns the representation of the deployment by contact of a stainless steel stent in an arterial tissue. The talk is based on joint works with Mikaël Barboteu and Serge Dumont (University of Perpignan, France).