The vectorial properties of paraxial beams propagating perpendicular to the optical axis of a uniaxially anisotropic crystal are investigated. By relying on a suitable planewave angular spectrum representation of the electromagnetic field, we obtain the analytical expressions of optical fields. The longitudinal component is expressible in terms of the first correction of the transverse field. Moreover, the extraordinary beams can induce ordinary beams in terms of the second correction of the transverse field.