Subharmonic vibrations of order 1/3 in stretched strings driven by a single‐mode planar simple harmonic force are investigated. It is shown that both planar and nonplanar subharmonic resonances can occur. Subharmonic vibrations are possible only if the amplitude of the force exceeds a certain critical value which depends upon the magnitude of the damping coefficient. The stability of the solution is analyzed, and it is shown that the region of stable nonplanar vibrations is wider than that of stable planar vibrations. It is also observed in the case of nonplanar vibrations that the amplitude of the subharmonic in the plane normal to the plane of the driving force is larger than that in the plane of the driving force.