We present a numerical method based on the linear elastic membrane theory to compute the morphological deformation of a spherical cell from the photonics stress distribution over the cellular membrane. The method is applied to fit the experimental data for deformation of a spherical human red blood cell trapped and stretched in a fiber-optical dual-beam trap with a single fitting parameter Eh where E is the Young's modulus of elasticity and h is the thickness of the cell membrane. We obtained Eh = (20+/-2)muNm(-1) which is comparable to results reported earlier. This numerical method can be applied in general experimental conditions.