Considering their similar mass densities, an attempt was made to optimize the mix design of micro-concrete that used barite sand as an aggregate by substituting marble powder (5%, 10%, 20%, 30%, 40%, 50%, 70%), clay brick powder (30%, 50%, 70%), and fly ash (30%, 50%, 70%) for the concrete (by mass) to form specimens for shaking table tests. The test results showed that for these three groups of materials, the substitutions had little effect on the density. The barite sand played a decisive role in the density, and the overall density of the specimens reached approximately 2.9 g/cm3. The compressive strength and elastic modulus decreased with an increase in the substitution rates for the three types of materials. Among them, the 28 day compressive strength values of the 40% and 50% marble powder groups were 11.73 MPa and 8.33 MPa, respectively, which were 58.7% and 70.7% lower than the control group, respectively. Their elastic modulus values were 1.33×104 MPa and 1.42×104 MPa, respectively, which were 39.1% and 35% lower than those of the control group, respectively. The 28 day compressive strength values of the 50% and 70% clay brick powder groups were 13.13 MPa and 5.8 MPa, respectively, which were 53.8% and 79.6% lower than the control group, respectively. Their elastic modulus values were 1.54×104 MPa and 1.19×104 MPa, respectively, which were 29.7% and 45.4% lower than those of the control group, respectively. The 28 day compressive strength values of the 50% and 70% fly ash groups were 13.5 MPa and 7.1 MPa, respectively, which were 52.5% and 75% lower than those of the control group, respectively. Their elastic modulus values were 1.36×104 MPa and 0.95×104 MPa, respectively, which were 37.9% and 56.6% lower than those of the control group, respectively. There was a linear relationship between the 28 day compressive strength and elastic modulus, with the correlation coefficient reaching a value higher than 0.88. The test results showed that the model materials met the high density, low compressive strength, and low elastic modulus requirements for shaking table tests, and the test data of the three groups of different alternative materials were compared and analyzed to provide references and assistance for relevant model testers.