This paper presents an exact 2-D analytical model for predicting the armature reaction magnetic field in idealized structures of permanent-magnet tubular linear machines with surface-inset mounted magnets. The armature reaction magnetic field distributions is analytically derived and compared to finite-element analyses. The analytical solution allows the prediction of the machine inductance and reluctance force in closed forms, and facilitates the evaluation of any possible partial irreversible demagnetization of the magnets. It can also be used to estimate resistance limited eddy-current losses in armature windings and permanent magnets. The developed analytical model can be advantageously used for the analysis and design of a class of linear tubular machines.