A mathematical model for describing the growth of a cylindrical particle caused by the effects of diffusion, interface kinetics and surface energy is employed to study the geometrical stability of the moving solid‐liquid interface. The results are obtained by using the sinusoidal perturbation technique to analyze the time dependent diffusion equation. The effect of perturbations in θ and z‐directions on radial growth are both considered. The results are consistent with those of previous work on the stability of a cylindrical particle due to diffusion control. The interface kinetics effects enhance the geometrical stability.