Computational aspects of the logarithmic strain space description are discussed and compared with se-called ''updated Lagrangian descriptions''. The shortcomings of the latter are demonstrated on an analytical example of homogeneous finite distortion kinematics. The numerical implementation and algorithms of the logarithmic strain space description with respect to the reference configuration are presented. Simulation results of two special purpose finite element programs, which are based on the logarithmic strain space description, are shown.