We consider an inertial (large Reynolds number) gravity current (GC) released from a lock of length $$x_0$$ and height $$h_0$$ into an ambient fluid of height $$Hh_0$$ which propagates along a channel with permeable floor and/or walls. The cross section (CS) of the container is defined by the general $$-f_1 (z) \le y \le f_2 (z)$$ for $$0 \le z \le Hh_0$$ , while the top and the bottom are at $$z = Hh_0$$ and $$z=0$$ (z is the physical coordinate measured from the bottom of the channel). We use Boussinesq assumption and formulate the shallow-water equations of motion. These equations include a parameter $$\lambda$$ which reflects the ratio between the typical time of propagation of the current over a length $$x_0$$ to the typical time of the drop of the interface due to porous boundary over a height $$h_0$$ . To solve the problem we employ the method of finite-differences. It is demonstrated that initially, the effect of a porosity of the floor or the walls on the distance of propagation of the GC is insignificant, but the “slumping” stage is absent. During the advanced stages, the porosity slows down the current and decreasing the effective distance of propagation. We illustrate the methodology for flow in symmetric channels with typical power-law CSs $$f_1(z) = f_2(z) = 0.5(c+bz^{\alpha })$$ , where $$b,c, \alpha$$ are non-negative constants and show that for the identical characteristics of the porous material, the presence of the porous floor has more significant effect on the velocity of the propagation of the current than the presence of the permeable walls in all tested forms of containers. Special attention is given to triangular CS channels $$f_{1}(z)=f_{2}(z) = bz$$ with permeable walls. We show that in such containers the volume of the current decreases like $$\exp \left( -\sqrt{1+\frac{1}{b^2}}\lambda t\right)$$ (where t is time) and for $$Hh_0 \gg 1$$ its run-out length can be expressed by a compact analytical formula.