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The paper is focused on computation of a compressive strength of composite materials by limit analysis. This method enables to determine the strength or other types of limit loads by solution of a specific optimization problem. It is also capable to predict failure zones. Abilities of the method are investigated on a particular composite -- a laboratory prepared sample consisting of a hard coal matrix and a polyurethane binder. This sample is chosen due to available CT images of the inner structure and laboratory experiments. Appropriate yield criteria are proposed for the coal and the binder in order to define the limit analysis problem. This problem is penalized and then discretized by higher order finite elements. For numerical solution, the semismooth Newton method and adaptive mesh refinements are also used. Numerical experiments in 2D for various CT scans and material parameters are performed.