The heart is modeled as a system of elastic and/or contractile fibers immersed in a viscous incompressible fluid. Simulated heart walls and valves are constructed by arranging the fibers according to an idealized version of the actual distribution of muscle fibers in the heart walls and collagen fibers in the valve leaflets. Then the combined motion of the fluid-fiber system is predicted through the numerical solution of its coupled equations of motion. Fluid equations are solved by a finite difference method on a fixed, regular computational lattice. Fiber points move freely through this lattice without being constrained to lie at the lattice intersections. Communication between fibers and fluid involves interpolation of the fluid velocity to the fiber points and the spreading of the fiber forces to the computational lattice of the fluid. Both of these operations make use of a smoothed approximation to the Dirac delta function. The entire method is suitable for implementation on vector, parallel, or parallel-vector hardware. Applications include the investigation of normal cardiac function, the simulation of disease processes affecting the mechanical function of the heart or its valves, and the computer-assisted design of prosthetic cardiac valves.