Abstract
The main objective of this work is to present some important results and formulas in the theory of Humbert matrix functions by using the concepts of matrix functional calculus. We define Humbert matrix functions assuming that not all the matrices involved are commuting. We show that these two variable Humbert matrix functions follow naturally as confluent cases of Appell matrix functions. We determine their regions of convergence, integral representations, transformation formulas, summation formulas, contiguous relations and matrix differential equations satisfied by them.