It is discussed how to understand the solution of the Dirichlet problem for the Stokes equations when the Dirichlet data are non-smooth such as if they are in L^2(Γ)^2 only. A weak solution (u, p) ∈ H^1(Ω)^2 × L^2(Ω) cannot be expected. Instead, the very weak formulation solution is considered, the solution is seeked in L^2(Ω)^2 × H^{−1}(Ω). Previous results on that topic are restricted to convex domains where the dual problem has a solution in H 2 (Ω)2 × H 1 (Ω) which is not true when nonconvex domains are considered. The corner singularities are carefully studied in order to obtain little more regularity than L^2(Ω)^2 × H^{−1}(Ω) such that the approximation error decreases when the mesh size tends to zero. Error estimates and numerical tests are presented.