Analysis of non-binary (K-ary, K > 3) information channels (IC) with memory as complex stochastic structures is rather complicated mathematically. Of significant interest is the synthesis of simplified mathematical models for such channels that allow clarifying relatively simply the most important regularities occurring in real processes. Modeling of IC (K-channels) with memory is a vital problem that has both theoretical and practical importance. In this paper models of discrete K-channels with memory are presented, their graphs of transition probabilities for various operating conditions built, and probabilities of outcomes of reception for symbols of the used alphabet estimated.