Most microfluidics-based sorting methodologies utilize size differences between suspended micro-objects as the defining characteristic by which they are sorted. Sorting based on mechanical properties, however, would provide a new avenue for sample preparation, detection and diagnosis for a number of emerging biological and medical analyses. In this study, we demonstrate separation of polystyrene (PS) and poly(methyl methacrylate) (PMMA) microspheres based entirely on their difference in mechanical properties using traveling surface acoustic waves (TSAWs). We theoretically examine the correlation of the applied TSAW frequency, particle density and sound speed with respect to the resultant acoustic radiation force (ARF) that acts to translate particles, and experimentally corroborate these predictions by translating PS and PMMA particles simultaneously in a stationary flow. Even when PS and PMMA particles have the same diameters, they exhibit strongly nonlinear and distinct acoustophoretic responses as a function of their mechanical properties and the applied TSAW frequency. By specifically matching the appropriate acoustic frequency to the desired particle size, each particle population can be selectively translated and sorted. We demonstrate that this mechanical property based sorting can continuously separate these particle populations with at least 95% efficiency in the mixed 10/15 μm diameter PS and PMMA particle solutions tested.