The onset of wrinkling of an unevenly stretched sheet metal subject to finite deformation is analyzed by an incremental finite element method. The sheet metal is modeled as a plate made of an elastic-plastic material. Hill’s anisotropic yield function and bifurcation criterion are employed in the analysis. The effects of geometrical and material parameters upon the onset of wrinkling are investigated. In the bifurcation analysis, attention is given to the changing and varying thickness of the sheet metal which could have a strong influence on the flexural rigidity of the sheet. Numerical results are presented herein.