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Thermal solidification processes are an important concern in today’s manufacturing technology. Because of the complex geometric nature of real‐world problems, analytical techniques with closed‐form solutions are scarce and/or not feasible. As a consequence, various numerical techniques have been employed for the numerical simulations. Of interest in the present paper are thermal solidification problems involving single or multiple arbitary phases. In order to effectively handle such problems, the finite element method is employed in conjunction with adaptive time stepping approaches to accurately and effectively track the various phase fronts and describe the physics of phase front interactions and thermal behaviour. In conjunction with the enthalpy method which is employed to handle the latent heat release, a fixed‐grid finite element technique and an automatic time stepping approach which uses the norm of the temperature distribution differences between adjacent time step levels to control the error are employed with the scale of the norm being automatically selected. Several numerical examples, including single and multiple phase change problems, are described.