Class I CH$_3$OH masers trace interstellar shocks. They have received little attention mostly as a consequence of their low luminosities; this situation has changed recently and Class I masers are now routinely used as signposts of outflows. The recent detection of polarisation in Class I lines now makes it possible to obtain information on magnetic fields in shocks. We make use of newly calculated collisional rates to investigate the excitation of Class I masers and to reconcile their observed properties with model results. We performed LVG calculations with a plane-parallel slab geometry to compute the pump and loss rates which regulate the interactions of the different maser systems with the maser reservoir. We study the dependence of the pump rate, the loss rate, and the inversion efficiency of the pumping scheme of Class I masers on the physics of the gas. Bright Class I masers are mainly high-temperature high-density structures with maser emission measures corresponding to high CH$_3$OH abundances close to the limits set by collisional quenching. Our model reproduces reasonably well most of the observed properties of Class I masers. The 25 GHz masers are the most sensitive to the density and mase at higher densities than other lines. Moreover, even at high density and high abundance, their luminosity is lower than that of the 44 GHz and 36 GHz lines. By comparison between observed isotropic photon luminosities and our model, we infer beam solid angles of ~0.001 steradian. Class I masers can be separated into 3 families: the $(J+1)_{-1}-J_{0}$-E type, the $(J+1)_0-J_1$-A type, and the $J_2-J_1$-E lines. The 25 GHz lines behave in a different fashion from the other masers as they are only inverted at densities above $10^6$ cm$^{-3}$ in contrast to other Class I masers. Therefore, the detection of maser activity in all 3 families is a clear indication of high densities.
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