Objective: The purpose of this paper is to investigate computationally the influence of sodium ion channel block on cardiac electro-mechanics. Methods: To do so, we implement a myofiber orientation dependent passive stress model (Holzapfel-Ogden) in the multiphysics solver Chaste to simulate an imaged physiological model of the human ventricles. A dosage of a sodium channel blocker was then applied and its inhibitory effects on the electrical propagation across ventricles modeled. We employ the Kirchhoff active stress model to generate electrically excited contractile behavior of myofibers. Results: Our predictions indicate that a delay in the electrical activation of ventricular tissue caused by the sodium channel block translates to a delay in the mechanical biomarkers that were investigated. Moreover, sodium channel block was found to increase left ventricular twist. Conclusion: A multiphysics computational framework from the cell level to the organ level was used to predict the effect of sodium channel blocking drugs on cardiac electromechanics. Significance: There is growing interest to better understand drug-induced cardiovascular complications and to predict undesirable side effects at as early a stage in the drug development process as possible.