We derive a linear moment tensor inversion method (which we call second nodal plane inversion) for obtaining a double couple focal mechanism when only one nodal plane is known. This typically is the case for shallow thrust events, for which only the steeply dipping nodal plane can be determined from teleseismic first-motions; conventional moment tensor inversion methods are known to fail for these events because the portion of the moment tensor corresponding to vertical dip-slip faulting is extremely inefficient in exciting surface waves. In this paper we invert long-period (256 s) fundamental mode Rayleigh waves from the IDA network; the inversion technique can also be applied to body wave amplitude data or to entire records (as a sum of normal modes), given the appropriate normal equations. We study several shallow (h<35 km) thrust earthquakes for which the steeply dipping nodal plane can easily be found from body wave first-motions. In contrast to standard surface wave moment tensor inversion techniques, which have serious stability problems for such shallow events, our technique sucessfully finds the scalar moment and second nodal plane.