A finite element viscoplastic computation is proposed where the strain dependent nonlinear stiffness matrix represents plasticity effects and a general nonlinear strain-rate dependent damping matrix accounts for the overall viscous loss. This model can assimilate any conventional plasticity data measured in the laboratory, where the loss coefficient is characterized by Q −1 . In field testing the same is estimated from seismological observations, usually stated as a strain, strain-rate (or frequency) independent loss factor. It is demonstrated herein that the solution of any auxiliary differential equation even for the constant Q model can be avoided when a Laurent series expansion is sought where the coefficients are calculated by a least square fit of the experimental Q- data . Therein the causality condition is satisfied exactly. Since the procedure yields an integro-differential equation the required time steps are considerably small as compared with those in standard explicit and implicit schemes.