In the welding of metal sheets by lasers or electric arcs, a problem of considerable interest and importance is the formation of stresses and strains in the material undergoing the welding process. This paper investigates the process making use of the linear theory of elasticity. The non-uniform heating of the metal is allowed for by the presence of an appropriate term in the stress tensor representing the temperature field. The weld pool is approximated by an elliptic region which is constant in cross sectional shape with depth. This paper calculates the stresses in metal outside the molten region in the frame of the laser using mainly analytical techniques and in its final stages evaluates these numerically for the cases of an unclamped as well as a clamped metal sheet. The results are found to be largely independent of the particular metal when the stresses are expressed in dimensionless form. The effects of welding the metal with a laser are essentially reversible in character when the analysis is restricted to linear elastic theory without phase changes.