A cross-slot microchannel has been harnessed for a wide range of applications, such as label-free measurements of cell deformability and rheological characterization of complex fluids. This work investigates flow kinematics in a cross-slot microchannel used for the measurements of cell deformability utilizing finite element method (FEM)-based numerical simulation. In a cross-slot microchannel, the cell is stretched near the stagnation of the cross-slot channel, and cell deformation is significantly affected by its trajectory. Two passive methods, inertia- and viscoelasticitybased, which do not rely on any external force such as an electric field, have been applied to focus particles along the channel centerline so that the cell trajectories are unified. However, it is not well understood how the flow kinematics inside the cross-slot channel is altered by the inertial or viscoelastic effect when these two methods are employed. This work demonstrates that the flow kinematics such as the distributions of flow type and strain rate is notably changed with an increase in the Reynolds number when an inertia-based method is employed. On the other hand, flow kinematics does not significantly deviate from that of an inertia-less Newtonian fluid irrespective of the Weissenberg numbers when a viscoelasticity-based method is used. The current work will be helpful for the design and operation of a cross-slot microdevice for measuring cell deformability.