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Optical tweezer is a non-contact tool to trap and manipulate microparticles such as biological cells using coherent light beams. In this study, we utilized a dual-beam optical tweezer, created using two counterpropagating and slightly divergent laser beams to trap and deform biological cells. Human embryonic kidney 293 (HEK-293) and breast cancer (SKBR3) cells were used to characterize their membrane elasticity by optically stretching in the dual-beam optical tweezer. It was observed that the extent of deformation in both cell types increases with increasing optical trapping power. The SKBR3 cells exhibited greater percentage deformation than that of HEK-293 cells for a given trapping power. Our results demonstrate that the dual-beam optical tweezer provides measures of cell elasticity that can distinguish between various cell types. The non-contact optical cell stretching can be effectively utilized in disease diagnosis such as cancer based on the cell elasticity measures.