The strength properties of jointed rock mass have attracted many researchers¢ attention in rock mechanics. In the paper,the fractured samples made by gypsum mixture containing two or three intermittent fractures with different allocations in the samples are loaded at different strain rates. In virtue of the sliding crack model(SCM) to simulate the branch crack propagation and using crack density method to consider interaction of multi-fractures,the uniaxial compressive strength of the fractured samples is analyzed at different strain rates. The studies show that the SCM can simulate the coalescence of cracks in tension and tension-shear mixed mode,but it isn¢t applicable to the shear coalescence mode;the strength properties of the fractured samples are not related to the pre-existed cracks in the fractured samples,but the coalesced cracks,i. e. controlled cracks. The variation of the strength of fractured samples vs. loading rates can be simulated through increasing the fracture toughness of the experimental material under low loading rate to medium loading rate condition,i. e. strain rates from 1.7×10-5 to 1.7×10-1 s-1. So,the SCM can be used to analyze the strength variation of the fractured media under low loading rate to medium rate condition and the variable of crack density can reflect the interaction of multi-fractures well.