In this paper, the strain effect on the morphological instability of the circular island is studied in terms of the BCF (Burton, Cabera, Frank) model. We introduce strains into the BCF model under the Gibbs-Thomson condition and investigate the instability of the island due to the combined effect of the misfit strain, applied strain, deposition flux, line tension, and the far-field flux. Thus, we obtain the perturbation growth rate and the critical deposition flux. Results indicate that the misfit strain and the far-field flux tend to destabilize the growth of the island, and the line tension has a stabilizing effect. In addition, the larger island is more stable during the growth of the island. Up to the critical radius, as the misfit strain increases, the critical flux increases. When taking into account the applied strain, the negatively applied strain stabilizes the growth of the island and decreases the critical flux. These results are almost opposite to the case of the positive strain. This could potentially provide on important theoretical basis for controlling the growth and stability of the films.