The objective of the present investigation is to develop the capability to predict creep properties of ceramic matrix composites (CMCs) from experimentally determined creep properties of the constituent phases. The particular composite system chosen consists of Textron SCS-6 SiC fibers embedded in a reaction-bonded silicon nitride (RBSN) matrix. Two approaches were employed to develop analytical models: finite element and rule-of-mixtures. The effect of multiaxiality was included using creep equations based on equivalent stress and equivalent strain. Predictions of the creep behavior of unidirectionally reinforced composites were carried out for longitudinal, transverse, and shear mechanical loadings. The rule-of-mixtures method was found to be capable of predicting macroscopic creep strains which were in good agreement with those predicted by the finite element method. Longitudinal creep strain predictions agreed well with the available experimental data. Stress redistribution between the fibers and matrix coincided with early stages of primary creep at elevated temperatures.