For any concerns of safe structural design, mechanical yield strength can be considered the most important material property to evaluate, a threshold not to cross to prevent plastic deformations to occur. It has been established that material’s strength depends strongly on the microstructure of the material. Most logically, the more porous the material, the weaker it is. In a more rigorous manner, Gurson (1977)[1] linked through a semi-analytical relationship the compaction cap of the yield surface with the porosity. However, a more generic framework to upscale for the yield strength of porous materials has been missing ever since. Therefore, a more profound understanding of the influence of the microstructure on material’s strength is lacking. For example, it can easily be shown that two different microstructures with the same porosity can achieve different strengths. As such, more morphological parameters of the microstructure need to be taken into account to describe material’s strength. In this contribution we present a Digital Rock Physics framework to upscale yield strength from microCT-scan images of rocks. The simulator implements 3D semi-discrete Finite Element elasto-plasticity. As a result, more features of the yield surface were attributed to the microstructure. Investigating further, the simulator was used to generate a database[2] of computed strength for microstructures of various rocks, characterised by an extensive list of their morphological parameters. With machine learning (Gaussian Processes with anisotropic kernels for Automatic Relevance Determination or Polynomial Chaos Expansion), we show that material’s strength could be explained mostly by the Minkowski Functionals of the microstructure but some minor morphological parameters, for example linked to the anisotropy of the microstructure, remain influential.