During mercury porosimetry experiments two of the most basic mechanisms responsible for mercury intrusion (drainage) into and retraction (imbibition) from porous media are meniscus intrusion into constrictions and thread snap-off in narrow pores, respectively. The present work consists of an experimental and theoretical study of these phenomena in model lenticular capillaries, that is, capillaries with lens-shaped cross section. The reason for this apparently strange choice is that several porous media of interest, such as sandstone reservoir rocks (and also model pore networks etched in glass plates and used in numerous experimental studies of multiphase flow in porous media) have pores of such type. The critical pressures for mercury intrusion and snap off in lenticular pores are measured experimentally and expressed in dimensionless form as functions of the pore aspect ratio (ratio of pore width to pore depth) and the contact angle. Analytical mathematical relationships are also developed for the calculation of these critical pressures. In the case of mercury penetration, very good agreement between experiment and theory is observed over the whole region of pore width to pore depth aspect ratio. In the case of mercury snap-off, very good agreement is observed for small and medium values of pore aspect ratio. A sizable discrepancy in the case of snap-off is observed in pores of large aspect ratio, and this is caused by the considerable deviation (in this case) of the pore shape of the experimental models from the lenticular one used in the theoretical calculations, as well as by the strong effect of the pressure of residual air on the values of measured pressures.