In this paper we model filters as networks of channels. As suspension (fluid with particles) flows through the filter, particles are trapped and clog channels. We assume there is no flow through clogged channels. The filter becomes impermeable after not all, but only a portion, of the channels clog. In this paper we compute an upper bound on the number of channels that clog. This bound is a function of properties of the network. Our results provide an understanding of the relationship between the filter pore space geometry and the filter efficiency