This is a study of the basic mechanical properties of specified density shale aggregate concrete, which is based on different replacement rates in stone-lightweight aggregate concrete (stone-LAC) and sand-lightweight aggregate concrete (sand-LAC). They were prepared by replacing the ceramsite and pottery sand with stone and river sand, respectively. Many tests were performed regarding the basic mechanical property indexes, including tests of cube compressive strength, axial compressive strength, splitting tensile strength, flexural strength, elastic modulus and Poisson’s ratio. The failure modes of specified density shale aggregate concrete were obtained. The effects of replacement rates on the mechanical property indexes of specified density shale aggregate concrete were analyzed. Calculation models were implemented for elastic modulus, for the conversion relations between the axial compressive strength and the cube compressive strength, and for the relations between the tension-compression ratio and Poisson’s ratio. It was shown that when the replacement rate of stone or river sand increased from 0% to 100%, the cube compressive strength of stone-LAC and sand-LAC increased, respectively, by 55% and 25%, the axial compressive strength increased, respectively, by 91% and 72%, splitting tensile strength increased, respectively, by 99% and 44%, and the flexural strength increased, respectively, by 46% and 26%. Similarly, the elastic modulus of stone-LAC and sand-LAC increased, respectively, by 16% and 30%. However, Poisson’s ratio for stone-LAC decreased first and then increased, eventually increased by 11%; Poisson’s ratio for sand-LAC only reduced gradually, eventually reduced by 67%. After introducing the influence parameter for the replacement rate, the established calculation models become simple and practical, and the calculation accuracies are favorable.