The paper is concerned with the decay properties of solutions of the Stokes equations with Neumann boundary conditions, which is obtained as linearized equations of the free boundary problem for the Navier-Stokes equations. In order to solve the Navier-Stokes problem local in time at least with small initial data, it is important to investigate the decay properties of solutions of the Stokes equations. In the problem considered here, the force at the boundary vanishes and therefore one can expect to get better decay properties of solutions compared with the nonslip boundary conditions case. Such better decay rate is derived in the estimate of gradients of the solutions of the Stokes problem. The problem is formulated in the analytical semigroup framework, and \(L_p\)-\(L_q\) estimates of the solutions are obtained.