This paper presents an effective numerical method of simulating the behaviour of a reaction-diffusion (RD) system on large dimpled skin surfaces. The simulation problem arises from models of initiation and development of hair follicles in sheep and other mammals. The numerical method has been selected to take advantage of the vector (pipelined) processing capability of a CDC Cyber 205 computer used for this work. The dimpled skin surface is mapped to a plane by a suitable coordinate transformation. A finite difference scheme is used to discretize the transformed RD system equations. Methods of solving the equations through time are discussed and a partly explicit and partly implicit Euler method is adopted. An iterative algorithm (successive overrelaxation with red-black ordering) is used to solve the implicit equations. The complete procedure is shown to be very computationally efficient on the Cyber 205.