The phenomenon of boiling crisis in a horizontal narrow annular geometry is analyzed by considering a buoyancy-driven two-phase flow in a vertical crevice. Conservation laws are formulated and solved analytically. A two-phase friction factor is determined using published experimental data. The effect of crevice axial length is also considered for a variety of working fluids. The predicting method based on the present work applies in wide ranges of annulus width and crevice length for a variety of fluids with a remarkable improvement in accuracy over the existing predicting methods.