The problem that arises during the movement of the shoreline in a sedimentary ocean basin is a moving-boundary problem with variable latent heat. A numerical method is presented for the solution of this problem. The differential equations governing the above process are converted into initial value problem of vector-matrix form. The time function is approximated by Chebyshev series and the operational matrix of integration is applied. The solution of the problem is then found in terms of Chebyshev polynomials of the second kind. The solution is utilized iteratively in the interface equation to determine time taken to attain a given shoreline position. The numerical results are obtained using Mathematica software and are compared graphically with the values obtained from a published analytical solution. (C) 2008 Elsevier Ltd. All rights reserved.