While coupled three-dimensional (3D) non-isothermal finite element (FE) models can be used to predict distortion in weldments, computational costs remain high and the development of alternate FE-based engineering approaches remains an important topic. In the present study, a plane stress model is proposed for analyzing angular distortion in butt welded plates having appreciable levels of weld reinforcement. The approach is based on an analysis of contractile shrinkage forces and only requires knowledge of the plastic zone geometry to develop the input data needed for an isothermal linear elastic FE model. Results show that the proposed method significantly reduces computational time and provides acceptable accuracy when plane stress conditions are satisfied. The effect of weld reinforcement was also analyzed using the method. Results indicate that the contraction force from the bead is dominant and that the primary effect of the crown is to increase eccentricity of the in-plane contraction force. A steel liner from a nuclear plant cooling tower was also analyzed to demonstrate the method. Results showed that the model was able to predict the distortion pattern and demonstrated fair accuracy.