The goal of this work is the development and numerical implementation of a mathematical model describing the functioning of heart valves. To couple the pulsatile blood flow with a highly deformable thin structure (the valve's leaflets), a resistive Eulerian surfaces framework is adopted. A lumped-parameter model helps to couple the movement of the leaflets with the blood dynamics. A reduced circulation model describes the systemic hemodynamics and provides a physiological pressure profile at the downstream boundary of the valve. The resulting model is relatively simple to describe for a healthy valve and pathological heart valve functioning while featuring an affordable computational burden. Efficient time and spatial discretizations are considered and implemented. We address in detail the main features of the proposed method, and we report several numerical experiments for both two-dimensional and three-dimensional cases with the aim of illustrating its accuracy. Copyright (C) 2015 John Wiley & Sons, Ltd.