A two-dimensional numerical study that models solidification of a pure metal in a horizontal crucible by using a finite-volume-enthalpy method has been carried out. The primary goals of the investigation are to assess the influence of phase change on the known transition to time-periodic convection and to predict the critical parameters associated with this phenomenon. Numerical simulations reveal the influence of the dimensionless solidification temperature Ts, on the critical value of the Grashof number Grcrit. The influence is found to be directly related to an effective aspect ratio of the liquid part of the cavity. When Tsis increased, it is found that oscillatory convection takes place at a higher Grashof number and with slightly higher frequency. However, varying the Stefan number Ste has small influence on the critical parameters. The critical value of Gr for the onset of the oscillation is determined by carrying out a series of time-dependant calculations.