This paper for the first time explores the application of the meshless approach, structured on the Local Radial Basis Function Collocation Method (LRBFCM), for solving the freezing process with convection in the liquid phase for a metals-like material in a closed rectangular cavity. The enthalpy one-domain formulation is used to avoid inclusion of additional boundary conditions at the fluid-solid interface. To avoid numerical instabilities, the freezing of a pure substance is modeled by a narrow phase change interval. The fluid flow is solved by a local pressure-velocity coupling, based on the mass continuity violation [1-3], and the explicit time stepping is used to drive the system to the free boundary solution. The results are presented through temperature and streamfunction contours and the liquid-solid interface position at the steady state, as well as the time development of the average Nusselt number and the time development of the cavity average liquid fraction. Results are validated with already benchmarked melting example . The paper represents first steps in solution of the Hebdich and Hunt experiment by an alternative numerical technique, different from the classical finite volume or finite element methods .