The mechanical behavior of the heart has been modeled for decades by using continuum mechanics and numerical methods. A widely used, but rarely discussed, assumption is that inertial effects can be neglected in these models. This M. Sc. project investigates the consequences of including inertial effects in modeling of left ventricular mechanics. A framework for simulating the complete cardiac cycle is implemented using the Python interface to FEniCS. Numerical experiments are performed to study the role of inertia. The constitutive model for the myocardium suggested by Holzapfel and Ogden will be used, along with a rule-based algorithm for assigning muscle fiber orientations to the ventricular geometry, by Bayer et al. Hozapfel and Ogden’s model assumes the myocardium to behave like an elastic material, despite strong evidence suggesting viscoelastic behavior. To see how inertial effects relate to rheology we propose a viscoelastic model for the myocardium, based on a generalization of the 1D Kelvin-Voigt material model. Employing the elastic model, while including inertial effects, led to unphysiological oscillations in the ventricular walls caused by the rapidly increasing pressure load during the diastole. The wall oscillations further led to oscillations in intraventricular volume and pressure. If instead the viscoelastic model is used, the wall oscillations are damped and no oscillations in the pressure and volume curves are observed.