In design of process equipment and hot vessel beam joints the real effect of relaxation is considered. Standards make an allowance that some relaxation of stresses at joint could be advantageous in relieving the stress peaks due to reaction moments. Magnitude of the moments in itself is not the problem but the stress distribution caused by it. The goal in this study is to estimate the possibility of taking advantage of relaxation in design using as test case a rectangular beam. Analytical theory of creep is applied with constant bending moment load. Stress distribution is first linear elastic and then flattens to nonlinear form resembling the elastic plastic bending. FEM gave analogous results constant moment and time dependent strain. One advantage is that fatigue life is increased at these joints after moderate amount of creep relaxation.