This work is concerned with the numerical approximation of the unsteady Stokes flow
of a viscous incompressible fluid driven by a threshold slip boundary condition of friction type.
The continuous problem is formulated as variational inequality, which is next discretize in time
based on backward Euler’s scheme. We prove existence and uniqueness of the solution of the time
discrete problem by means of a regularization approach. Finally, we derive error estimates that
justify the convergence property of the discretization proposed.