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We aim at analysing fluorescence microscopy sequences of moving cells, so as to estimate the velocities that define the movement, the forces that drive this movement, and the pressure that characterises the material state. We use an optical flow method constrained by Stokes flow mechanics equations that define the dynamics of a fluid that is incompressible, homogeneous and viscous. We present a finite element formulation that leads to a quadratic programming problem. We apply the method to real biological data of amoebas observed by fluorescence microscopy.