Organ-on-a-chip devices can be used to control and monitor the cellular microenvironment of human microtissues, providing a promising platform for disease and drug development studies. Here we describe a heart-on-a-chip system combining human induced pluripotent stem cell derived cardiomyocytes with microfluidic technology as a cardiotoxicity screening platform (Mathur et al. Sci. Rep. 2015). Within this microphysiological system, image tracking techniques can be used to monitor important indicators of cardiac function, such as contraction velocity, beat rate, and prevalence (Huebsch et al. Tissue Eng. C. 2015). However, mechanical contraction properties such as force and stress are harder to capture. This motivates the need for a numerical model simulating the mechanical behavior of the microtissue, to predict and help monitor the effect of drugs and mutations on the contractility of the tissue. In this study we propose a model for cardiac tissue applied to a geometric representation of the chip system to predict contraction forces and strain. We are using a zero-dimensional point model of cardiac myofilaments developed by Rice et. al. (Biophysical Journal 2008) to calculate the force generated by single myocytes, embedded within a continuum model for the mechanics of ventricular myocardium given by Guccione et. al (ASME 1991). Combined, this give us a system of partial differential equations, which we solve using the finite element method over a given three-dimensional mesh. The parameters in the model are optimized using data from real heart-on-a-chip devices. We evaluated the system for pharmacology studies (as of now, negative and positive inotropes respectively flecainide and isoproterenol) using experimentally measured calcium amplitude transients to predict resulting Cauchy stresses at increasing drug doses. Combining our numerical model for mechanical simulation with experimental heart-on-a-chip data produced comparable dose response results. We observed similar trends for measurements of internal forces of the tissue under isometric conditions. This combined in silico / in vitro analysis system provides the possibility of a robust technique for understanding the physiological complexity of micro-organ function in vitro, facilitating contraction force assessment for drug screening and disease modeling in heart-on-a-chip systems.