This paper reports on a GaN/Si surface acoustic wave (SAW) impedance element filter operating in the few gigahertz region. The PI-type filter consists of three SAW resonators with the same digit/interdigit widths, integrated with series/parallel planar inductors. The design procedure is based on modeling the SAW resonators using four parameters, independent of the equivalent circuit model representation (series resonance frequency, static capacitance, quality factor, and effective coupling coefficient). The series frequency is tuned by a planar inductor placed in series, while the parallel resonant frequency is tuned by a planar inductor placed in parallel with the SAW resonator. Closed-form equations are derived for the analysis of lumped-element SAW resonators. The design procedure is further based on the area of the SAW resonator and the lengths of the planar inductors as independent variables. Full-wave electromagnetic and circuital co-simulations and parametric optimizations are employed for the final filter design, which is implemented in the coplanar waveguide topology. The lumped-element SAW bandpass filter is fabricated using e-beam lithography for the definition of the 200-nm-wide interdigital transducers. Measurement results show the insertion losses of 12.9 dB at 5.49 GHz, the return losses of 16 dB, 3-dB bandwidth of 8.3 MHz, and the out-of-band rejection of 24 dB. The filter is compatible with monolithic integration with GaN active electronics.