In this talk we show how to describe the set of invariant measures of non- minimal substitution tiling systems in terms of their substitution matrices. It is known that for primitive substitutions, the associated tiling system is minimal, uniquely ergodic and the unique invariant probability measure is determined by the direction of the positive eigenvector of the substitution matrix. In the general case, the substitution matrix can be decomposed into irreducible components which determine the finite and some natural infinite invariant measures. This is a joint work with Boris Solomyak.