The problem of optical saturation of intersubband absorption has attracted considerable attention recently. The problem is very important to the development of superlattice devices such as fast infrared detectors and modulators because one needs to know the range of input optical intensities for which linear operation is possible. The linear and the third-order nonlinear optical intersubband absorption coefficients in hyperbolic quantum wells are studied,where emphasis is devoted to the influence of the shape of the wells on the absorption coefficients. The analytic forms for the linear and the third-order nonlinear optical intersubband absorption coefficients are derived by means of the density matrix formalism taking into account the intrasubband relaxation. Finally,the numerical results show that the optical absorption coefficients depend on the shape of the wells,the tunnel bandwith and the optical intensity.