In Performance-Based Earthquake Engineering, responses of structures are computed by nonlinear response history analysis under an appropriate set of ground motions. Based on the computed demand parameters, probabilities for exceeding certain limit states usually defined in terms of the peak deformation corresponding to appropriate intensity measures are estimated. This critical step in seismic design is known as fragility analysis. Seismic demand might be appreciably amplified under two orthogonal horizontal components relative to the unidirectional companion. Variability of record-to-record and the uncertainties of various parameters governing structural response may play an important role in this fragility analysis. Against this backdrop, the Bayesian linear regression model based seismic fragility has evolved for unidirectional seismic shaking. This is extended in the current study to account for bidirectional excitation for single degree of freedom systems. This also confirms the significance of bidirectional shaking.