Quadrupole acoustic logging is used to measure shear in the logging-while-drilling (LWD) environment. Evaluation of shear slowness in quadrupole acoustic logging requires an inversion method that takes into account the dispersion of the quadrupole mode, including tool-presence effects. The inversion method was developed to adopt a semblance processing that is based on waveform back propagation, assuming a homogeneous isotropic (HI) formation model with tool-presence effects. The inversion optimizes formation shear slowness and also includes optimization of mud slowness as an internal parameter to compensate for effects of undetermined mud slowness. A fast and robust optimization technique was employed using characteristics of the quadrupole semblance map to locate the maximum semblance peak. An automatic frequency band selection minimized errors from unknown borehole parameters and environmental effects. Testing with synthetic data validates the inversion method and field results showed very good agreement with wireline measurements.