A new model for predicting the uniaxial stress-strain behavior of a unidirectional ceramic matrix composite, including stochastic matrix crack evolution, stochastic fiber damage, and ultimate failure, is presented. The model shows that (i) "brittle" behavior (low failure strain) occurs when the matrix cracking stresses are sufficiently high and at a strain that is controlled by the matrix flaw population and elastic properties while (ii) "tough" behavior (high failure strain) occurs when the matrix cracking stresses are lower, and at a failure strain controlled by the fibers. In both cases, the failure strength is fiber-controlled. Applications to SiC/SiC composites have been made in a separate publication. Here, the model is used to demonstrate how changes in interfacial tau change the stress-strain curve, failure strain, and tensile strength when the underlying matrix and fiber flaw distributions are held fixed.