Numerical analysis is made of the structure of one‐dimensional unsteady magnetic compression waves propagating into collisionless plasmas when the ambient magnetic field is oblique to the wave direction. Integration of the equations of motion is carried out by dividing the flow field into discrete elements or slabs of plasma and following their motion on a digital computer. Results from these calculations show that both the sub‐ and supercritical solutions change continuously from one limiting situation to the other. A similarity rule is found for correlating the subcritical cases so that the two‐parameter family of solutions in mass ratio and field angle are reduced to a single set.