Cell performance is of great interest in a variety of biological processes and bioengineering applications, such as the cell motion in a manipulating biochip, and the cell deformation in a capillary. The present research work focuses on the numerical investigation of the motion and deformation of a single cell or two cells in the parabolic hydrodynamic field, nonuniform electric field, and parabolic hydrodynamic and nonuniform electric coupled field, respectively. A two-fluid model is presented to describe the flow characteristics of cell suspending in a fluid, considering the interactions between the cell and hydrodynamic field, between the cell and electric field, and between the two cells. The shell model is adopted to describe the interaction between the cell and hydrodynamic field, identified by the membrane mechanical force, where the cell membrane is treated as an incompressible and elastic shell with a uniform thickness and allowed to undergo the stretching and bending deformation. The Maxwell stress tensor (MST) approach is used to describe the interaction between the cell and electric field, identified by the dielectrophoresis (DEP) force due to the cell polarization. The Morse potential model is employed to describe the interaction between the two cells, identified by the intercellular interaction force behaving as a weak attractive force at far distance but a strong repulsive force at near distance. As the first academic achievement made in this thesis, the two novel numerical methods are developed to efficiently treat the two-fluid model, namely the modified particle binary level set (MPBLS) method for tracking the cell membrane, and the