A method of making frac sand having a selected grade from a naturally occurring, mined sand having a SiO2 content of at least about 80 percent and having a particle size range where the maximum particle size is less than about 8.0 mm, comprising: crushing the mined sand into an intermediate particulate material; screening the particulate material into a feedstock with particles having a particle size coarser than about 350 mesh and initial values for roundness and sphericity of the particles; passing the particles of the feedstock through a blast tube with an outlet to pneumatically abrade the particles and propel the feedstock in a stream under a given pressure from the outlet; directing the pressurized stream against a fixed target located at a given distance from said outlet to physically abrade the particles to form an output mass containing abraded particles: and, repeating operations (c) and (d) a number of times or process stages until the particles resulting from the repeatedly abraded output mass is a final output mass having both processed roundness and sphericity values of at least 0.6 and wherein the values are greater than the initial values of the feedstock by at least about 0.10 to 0.50.