A family of phosphate glasses has been developed with thermal expansion behavior in the elastic range that nearly matches the response of 304 stainless steel. Attempts to make concentric pin-shell seals consistently have yielded fractures between 400° and 300°C during cooling. Elastic stress analyses which neglect glass transitional behavior and utilize constant glassy (elastic) thermal expansion coefficients predict a residual stress state that is compressive. However, viscoelastic computations which include the effects of structural relaxation during glass transition show that tensile stresses sufficient to cause failure arise during cooldown of the seal.