Objective: Unidirectional conduction block in the heart can occur at a site where the impulse is transmitted from a small to a large tissue volume. The aim of this study was to evaluate the occurrence of conduction block in a 2-dimensional and 3-dimensional computer model of cardiac tissue consisting of a narrow strand abruptly emerging into a large area. In this structure, the strand diameter critical for the occurrence of block, hc, was evaluated as a function of changes in the active and passive electrical properties of both the strand and the large medium. Methods: The effects of changes in the following parameters on hc were analysed: (1) maximum sodium conductance (gNamax), (2) longitudinal (Rx) and transverse (Ry) intracellular resistivities, and (3) inhomogeneities in gNamax and Rx and Ry between the strand and the large area. Three ionic models for cardiac excitation described by Beeler-Reuter, Ebihara-Johnson, and Luo-Rudy ionic current kinetics were compared. Results: In the 2-dimensional simulations, hc was 175 μm in Ebihara–Johnson and Beeler–Reuter models and 200 μm in the Luo–Rudy model. At the critical strand diameter, the site of conduction block was located beyond the transition, i.e. a small circular area was activated in the large medium, whereas with narrower strands conduction block occurred within the strands. The decrease of gNamax resulted in a large increase of hc. This increase was mainly due to the change of gNamax in the large area, while hc was almost independent of gNamax in the strand. Changing Rx had no effect on hc, whereas the increase of Ry decreased hc and reversed conduction block. Inhomogeneous changes of Rx and Ry in the strand versus the large medium had opposite effects on hc. When the resistivities of the strand alone were increased, hc also increased. In contrast, the increase of the resistivities in the large area reduced hc. In the 3-dimensional model, hc was 2.7 times larger than the corresponding 2-dimensional values at the various levels of gNamax and resistivity. Conclusions: (1) At physiological values for active and passive electrical properties, hc in the 2D simulations is close to 200 μm in all three ionic models. In the 3-dimensional simulations, hc is 2.7 larger than in the 2-dimensional models. (2) The excitable properties of the large area but not of the strand modify hc. The decrease of intercellular coupling in the large medium facilitates impulse conduction and reduces hc, while the same change in the strand increases hc. (3) Occurrence of conduction block at an abrupt geometrical transition can be explained by both the impedance mismatch at the transition site and the critical curvature beyond the transition. © 1995 Elsevier Science B.V. All Rights Reserved.