Let \( \Omega \subset R^m\) be a bounded domain with boundary \( \Gamma \) of class \( C^{2,1}\). Choose \( T_1,\dots ,T_k\in \Gamma \) and \( \lambda_1,\dots ,\lambda_k\in R^1\) such that \( \lambda_1 +\lambda_2+\dots +\lambda_k =0\). The paper studies a very weak solution \( (u^0,p^0)\in L^r(\Omega )^m\times W^{-1,r}(\Omega )\) of the Stokes problem \( -\Delta u^0+\nabla p^0=0\), \( \nabla \cdot u^0=0\) in \( \Omega \), \( u^0=\sum_{j=1}^k \lambda_j \delta_{T_j}\) on \( \Gamma \). Here \( \delta_x\) is the Dirac measure concentrated in \( x\). It is shown that the solution of the problem is approximated by weak solutions of the problem \( -\Delta u^\epsilon +\nabla p^\epsilon =0\), \( \nabla \cdot u^\epsilon =0\) in \( \Omega \), \( u^\epsilon =g^\epsilon \) on \( \Gamma \). Here \( g^\epsilon \) are continuous functions on \( \Gamma \) which converge in some sense to \( \sum_{j=1}^k \lambda_j \delta_{T_j}\).