Abstract: For both medical and radiographic standing wave linear accelerators, a small beam spot diameter is always pursued. In order to minimize the size and weight of the machine and reduce the power dissipation, rf focusing is preferred to the focusing solenoid coil. Therefore, it is important to study behaviours of beam transverse motions in the rf fields for the design of SW linacs. Our research shows that the transverse motion behaviours of the electron beam in the compact linac is mainly determined by the rf field distribution of the first banching cavity and injection conditions of the beam. In this paper, a beam envelope equation is presented, the properties of the E₂, E₁, H₀ field distributions of various first bunching cavities of both symmetric and asymmetric are studied, and then the rf electric force and rf magnetic force exerting on the beam with a different injection time are analysed. It is demonstrated that the asymmetric first bunching cavity with a small gradient of E₂(z) field will provide a larger transverse emittance. And an asymmetric cavity with a larger front aperture and a small back aperture is favourable to make a smaller gradient of E₂(Z) field. For both symmetric and asymmetric first bunching cavity, by adopting an appropriate negative injection angle the envelopes of the beam are all decreased obviously, the optimum injection angle being always around -3°. The measured result of the beam spot of a 4MeV SW linac shows that the above mentioned simulation calculation of the radial dynamics is in good agreement with the measured result.