We present an experimental and analytical study of resonances in the current-voltage characteristics of single and double row triangular Josephson arrays. The magnetic-field dependences of the voltage positions of the resonances have been measured for various cell inductances and junction critical currents. In double row arrays, we have observed a peculiar resonance, whose voltage position decreases with magnetic field. We derive the spectrum of linear electromagnetic waves propagating in the arrays. In the double row array, the spectrum consists of many branches that differ by the behavior of the Josephson junctions transverse to the bias current direction. The measured magnetic-field dependence of the resonance voltages is mapped to the linear mode spectrum and good agreement between experiments and model is found.