Deep drawn shapes with orthogonal wall components are usually evaluated by shape accuracy and visual quality. There have been only a few investigations on the stability of such structures; however, the effect of the wrinkles on the stability of the wall is important for packaging applications and can support the shape accuracy. This paper focuses on the influences of process parameters on the stability of orthogonal walls of shapes produced by deep drawing with rigid tools and immediate compression. The wall stability was evaluated by tensile testing orthogonal to the direction of the wrinkles. The stability distribution was characterized with regard to the drawing height, and a comparison was made between the two different materials. The wall stability decreased with increases in the forming height. Furthermore, a blank holder force design and z-directional compression level improved the wall stability. Together with an elevated moisture content of the material and thermal energy supply that delivered two to three times higher resistance against wrinkle extension, these effects drastically improved the wall stability.