Finite element analysis is performed for transient thermal deformation of a shadow mask inside the Braun tube and the landing shift or mislanding of the electronic beam is calclated. The shadow mask has numerous slits through which the electronic beams are guided to land on the designed phosphor. Its thermal deformations therefore cause the mislanding of the electronic beam and result in decolorization of a screen. For realistic finite element analysis, firstly the effective thermal conductivity and the effective elastric modulus are calculated, and the shadow mask is modeled as shell without slits. Next the nonlinear finite element formulation is developed for transient heat transfer on the shadow mask, wherein thermal radiation is a major heat transfer mechanism. Analysis of the resulting thermoelastic deformations is followed, from which the mislanding of the electronic beam is obtained. The present finite element scheme may be efficiently used for thermal deformation design of a shadow mask.