Mammals have an evolutionary history spanning hundreds of millions of years. Today, mammals represent one of the most diverse groups of tetrapod vertebrates. In particular, they present a great postural diversity. The humerus adopts different positions: small mammals have a "crouched" posture with a quasi-horizontal humerus, while in the largest species, the humerus is more vertical. Some monotremes have more transversely oriented humeri similar to those of reptiles. The forelimb of moles is also modified in relation to their burrowing lifestyle. This postural diversity is accompanied by an important microanatomical disparity. Indeed, the bones of the appendicular skeleton support the weight of the body and are subjected to various forces that partly shape their external and internal morphology. We show here how geometric and microanatomical parameters measured in cross-section such as the polar section modulus or the position of the medullo-cortical transition can be related to posture. Using statistical methods that take phylogeny into account, we develop a postural model from a sample of humerus cross-sections belonging to 41 species of extant mammals. Our model can be used by palaeontologists to infer the posture of extinct synapsids. As an example, we infer the posture of two emblematic taxa: Dimetrodon natalis and Peratherium cuvieri. The results of the analysis indicate a sprawling posture for Dimetrodon and a crouched posture for Peratherium. This work contributes to unravel the complex interaction between phylogeny, humeral microanatomy and geometry, body mass, lifestyle and posture in mammals.