This paper introduces a semi‐analytic finite element technique for predicting standing wave motions (critical speed phenomena) in pneumatic tires. A general formulation is presented which encompasses inflation and rotation of the tire as well as vibratory motions superimposed upon the inflated and rotating state. The use of sinusoidal basis functions for the circumferential variation of each displacement component reduces the finite element model to two dimensions and improves solution accuracy for higher‐frequency modes. Under suitable assumptions, the harmonic components uncouple, and the three‐dimensional problem may be solved as a sequence of smaller two‐dimensional analyses. The proposed technique provides improved accuracy over three‐dimensional analysis at a small fraction of the cost and modeling effort.