A theory to describe the evolution of multiple matrix cracking in brittle matrix composites is presented. The theory is based on the similarity between multiple matrix cracking and fiber fragmentation in a single-fiber composite, a problem recently addressed by the present author. Assuming a critical strain criterion for matrix cracking, the number of matrix cracks vs applied stress and the distribution of crack spacings at saturation are shown to depend on the statistical distribution of initial flaws in the material and the material constituent properties, particularly the fiber/matrix interfacial sliding resistance tau. Hence, using the theory to fit experimental data on multiple cracking leads to a deduction for the value of tau. Application of the theory to recent data on Nicalon fiber/CAS glass composites yields estimates of tau = 19 and 22 MPa on two different samples. These values of tau are close to some estimates obtained by other approximate means but in disagreement with other estimates, and the origin of the discrepancy between various values of tau is as yet unresolved.