Appropriate mechanical representation of passive muscle tissue is crucial for human body impact modelling. In this paper the experimental and modelling results of compressive loading of freshly slaughtered porcine muscle samples using a drop-tower testing rig are reported. Fibre and cross-fibre compression tests at strain rates varying from 11,600%/s to 37,800%/s were performed. Experimental results show a nonlinear stress-stretch relationship as well as a clear rate dependency of the stress. The mean (standard deviation) engineering stress in the fibre direction at a stretch of 0.7 was 22.47 kPa (5.34 kPa) at a strain rate of 22,000%/s and 38.11k Pa (5.41 kPa) at a strain rate of 37,800%/s. For the cross-fibre direction, the engineering stresses were 5.95 kPa (1.12 kPa) at a strain rate of 11,600%/s, 25.52 kPa (5.12 kPa) at a strain rate of 22,000%/s and 43.66 kPa (6.62 kPa) at a strain rate of 37,800%/s. Significant local strain variations were observed, as well as an average mass loss of 8% due to fluid exudation, highlighting the difficulties in these kinds of tests. The inverse analysis shows for the first time that the mechanical response in terms of both applied load and tissue deformation for each of the strain rates can be captured using a 1st order Ogden hyperelastic material law extended with a three-term quasilinear viscoelastic (QVL) expansion to model viscoelastic effects. An optimisation procedure was used to derive optimal material parameters for which the error in the predicted boundary condition force at maximum compression was less than 3% for all three rates of testing (11,600%/s, 22,000%/s and 37,800%/s). This model may be appropriate for whole body impact modelling at these rates.