It is pointed out that simple models adopted so far have tended to neglect the obliquity of the magnetic field lines entering the Earth's surface. A simple alternative model is presented, in which the ambient field lines are straight, but enter wedge shaped boundaries at half a right-angle. The model is illustrated by assuming an axially symmetric, compressional, impulse type disturbance at the outer boundary, all other boundaries being assumed to be perfectly conducting. The numerical method used is checked from the instant the excitation ceases, by an analytical method. The first harmonic along field lines is found to be of noticeable size, but appears to be mainly due to coupling with the fundamental, and with the first harmonic across field lines.<br><br><b>Key words.</b> Magnetospheric physics (MHD waves and instabilities).