Goodman and Bray's kinematic model of common toppling can be extended to show that the maximum angle between the slope and the dip direction of the penetrative discontinuity that allows toppling depends on the friction angle of the discontinuities and the angle of the slope when the discontinuities dip into the slope. Flexural toppling can occur when the discontinuities dip in the same direction as the slope but more steeply than the slope and the angle of friction on the discontinuities. Natural examples of toppling in these extended ranges of orientations occur. Key words: toppling, discontinuity, rock slope, anaclinal, cataclinal, plagoclinal, orthoclinal, underdip.