We present a method for size-independent manipulation of elastic polystyrene (PS), poly(methyl methacrylate) (PMMA), and fused silica (FS) microspheres that uses travelling surface acoustic waves (TSAWs). Normally incident TSAWs originating from an interdigitated transducer (IDT) were used to separate similar-sized pairs of PS and PMMA or PS and FS elastic particles by producing distinct lateral deflections across laminar streamlines in a continuous flow microfluidic channel. Elastic particles with similar diameters but different acoustic impedances exhibit significantly different deflection characteristics when exposed to TSAW-based acoustic radiation forces (ARFs). For instance, exposing a mixture of PS and PMMA particles with similar diameters ($5 mm) to TSAWs with frequencies of 140MHz and 185 MHz produces larger deflections of the PS and PMMA particles, respectively. This difference arises because of the resonance of the elastic particles with the incoming acoustic waves at certain frequencies. Similar particle deflection characteristics were observed for mixtures of PS and FS particles with comparable diameters (3/3, 4.8/5, 10/10 mm). This difference in deflection distances was used to experimentally characterize the non-linear behavior of the ARFs acting on particles (3-10 mm) exposed to a range of TSAW frequencies (120-205 MHz). Our experimental results can be explained by plotting the acoustic radiation force factor (F F ) against the TSAW frequency (f TSAW ) and the dimensionless Helmholtz number (1 < k < 4), which is calculated by using a theoretical model of an elastic microsphere suspended in a fluid.