The elastic supported block ballastless track has several disadvantages, such as major dynamic gauge variation and moderately weak track geometry retention capacity. Hence, a slope elastic supported block ballastless track is proposed. The rail and support  block deformation, the support block displacement relative to the support block groove, and the support block and track bedplate stress state are analyzed using the static calculation method to estimate the reasonable slope of the short side of the elastic support block. Based on the simulated axle drop test, the stiffness matching of components of a slope elastic supported block ballastless track is further examined. The results show that the slope elastic support block is better for controlling the track structure deformation and improving the stress state, such as support block, rubber boots, and track bedplate. It is proposed that, when the axle load is less than 30 tons, the slope value of the short side of the elastic support block should be 1∶5 to 1∶6, the boot stiffness should be approximately 200 kN/mm, and the stiffness of the bedplate under the block should be approximately 80 kN/mm.