The operation of the plasma resonance probe in the absence of a magnetic field is now well understood, and the resonant frequency can be interpreted to give the electron density in the plasma. In many potential applications of this diagnostic technique to laboratory and space plasmas, a static magnetic field is present. This paper considers the resulting modifications to the resonance. The analysis is based on the simplified model of the probe behavior that has been validated for the zero magnetic field case by the work of Harp and Crawford. It is concluded that the technique can be applied to obtain the electron plasma frequency &ohgr;pand the electron density for&ohgr;c2≪&ohgr;p2; and the electron cyclotron frequency &ohgr;c, and hence the local magnetic field when&ohgr;c2≫&ohgr;p2. An approximate correction formula is derived for the intermediate range&ohgr;c2≈&ohgr;p2.