Using a viscoelastic liquid droplet model for modeling leukemia cells, and solvent viscosity and polymeric viscosity to model cytosol and cytoskeleton, I simulated migration of encapsulated leukemia cells in a constricted microcapillary. I studied deformation of three different encapsulated leukemia cells, including: HL60, Neutrophil and Jurkat in a constricted microcapillary. The simulations showed that the three leukemia cells elongated while passing through the microchannel constriction and regained their shape downstream of the channel. However, their deformation characteristics were different, with the Jurkat cells being the least viable with dramatically high deformation at low polymer concentration due to their lower cortical tension compared to that of the other two cells. Viscoelasticity and size of the encapsulating droplet as well as the constriction narrowness and length were found to impact the cell deformation which were tailored to improve the viability of cells. This work showed the importance of cell type, morphogenesis of the shell fluid materials and other physical properties on dynamics of cell migration in microchannels.