Structural surface texturing is believed to be a promising approach to modify tribological and thermal performances of tooling for sheet-stamping processes. However, a fundamental study on the surface-texturing design and resulting material deformation is currently lacking. In this paper, an advanced analytical buckling model specifically for the utilisation of textured tools at macro-scale, comprising dislocation-driven material model, isotropic yield criteria, bifurcation theory and Donnell-Mushtari-Vlasov (DMV) shell structure theory, was established. The developed analytical buckling model was validated by cylindrical deep-drawing experiments. Further finite element (FE) simulations with the implementation of material model via user-defined subroutine were also used to validate the bucking model for large surface texture designs. Effects of theoretical assumptions, such as yield criterion, boundary condition and test-piece geometry, on the accuracy of model prediction for wrinkling were investigated. It was found that the von Mises yield criterion and hinged boundary condition exhibited more accurate predictions. In addition, the DMV shell theory made this model most representative for large structural texturing designs. Furthermore, the implementation of induced shear strain component has an important effect on precisely predicting the wrinkling occurrence. The advanced analytical models developed in this study combine various classical mechanics, structure stability and material modelling together, which provides a useful tool for tooling engineers to analyse structural designs.