Mechanical behavior of the heart muscle tissues is the central problem in finite element simulation of the heart mechanics. Nonlinear elastic and Viscoelastic behaviors and their constitutive relations are determined from experimental data in order to characterize the passive response of the left ventricular myocytes (muscle cells) taken from guinea pig heart. Uniaxial tension test was made to determine the constants of the nonlinear elastic model (hypoelastic) in which Eulerian or exponential stress-strain relationship was assumed to describe the passive response of the heart material. Nonlinear elastic behavior was also described by hyperelastic strain energy functions such as Ogden models and Mooney–Rivlin models and the corresponding energy functions coefficients were determined. Stress relaxation test was conducted to assess relaxation behavior as well as viscosity of the tissues. Viscohyperelastic behavior was constructed by a multiplicative decomposition of a standard Mooney-Rivlin or Ogden strain energy function,W , for instantaneous deformation and a relaxation function,  tR , in a Prony series form. Nonlinear least square fitting and constrained optimization was conducted under MATLAB and MARC in order to obtain the material constants. From the physics of heart motion we found that hypoelastic or hyperelastic behaviors could be safely used for heart mechanics simulation, because the characteristic relaxation time is very large compared with the actual time of heart beating cycle. To get more precise mechanical properties, needed for very accurate bio-simulation and development of new material for artificial heart, an optimization algorithm was proposed to correct and estimate material parameters from clinical intact heart measurements.