Free and moving boundary problems require the simultaneous solution of unknown field variables and the boundaries of the domains on which these variables are defined. There are many technologically important processes that lead to moving boundary problems associated with fluid surfaces and solid-fluid boundaries. These include crystal growth, metal alloy and glass solidification, melting and flame propagation. The directional solidification of semi-conductor crystals by the Bridgman-Stockbarger method 1,2 is a typical example of such a complex process. A numerical model of this growth method must solve the appropriate heat, mass and momentum transfer equations and determine the location of the melt-solid interface. In this work, a Chebyshev pseudospectral collocation method is adapted to the problem of directional solidification. Implementation involves a solution algorithm that combines domain decomposition, a finite-difference preconditioned conjugate minimum residual method and a Picard type iterative scheme. © 1994, MCB UP Limited. All rights reserved.