An expression is derived for numerical computation of the symbol error probability of 16-ary offset quadrature amplitude modulation with sinusoidal shaping (16-ary offset-QAM). The channel considered here is a nonlinear satellite channel with additive Gaussian noise (AGN) in both up-link and down-link. The main source of the nonlinear distortion in two-link satellite channels is the travelling wave tube (TWT) power amplifier on-board of the satellite. The transponder nonlinearity considered in this paper is of the band-pass type (BPNL), which introduces a nonlinear input-ampliutde to output-amplitude (AM-to-AM) distortion and nonlinear input-amplitude to output-phase (AM-to-PM) distortion . Finally, a comparative study of 16-ary QAM and 16-ary offset QAM with sinusoidal shaping is performed with the BPNL operated at various levels of back-off from saturation.