The regularised long wave equation is solved by Galerkin's method using linear space finite elements. In the simulations of the migration of a single solitary wave, this algorithm is shown to have good accuracy for small amplitude waves. Moreover, for very small amplitude waves (less than or equal to 0.09) it has higher accuracy than an approach using quadratic B-spline finite elements within Galerkin's method. The interaction of two solitary waves is modelled for small amplitude waves. (C) 2002 Elsevier Science Inc. All rights reserved.