A three-dimensional model of myocardial tissue has been developed which incorporates electrotonic interactions between neighbouring myocytes. The algorithms of the model are based on asynchronous planning of discrete events. Each cellular element is described in a logical way and traces a predefined action potential which is dynamically modified depending on the electrotonic interactions. The model has a low computational complexity and has been implemented on personal workstations even for experiments investigating arrhythmogenic processes and simulating several tens of cycles in blocks composed of several thousand elements. The paper describes the algorithmic implementation of the model and presents three series of experiments examining the dependence of the accuracy of the model on the size of the modelled tissue, changes of the shape of simulated T-waves due to electrotonic interactions and arrhythmogenic processes caused by lowering the threshold of the electric flow which excites individual cells.