ABSTRACT: A brief review of the Algebraic Bethe Ansatz (ABA) technique and the application to integrable models with staggered disposition of R-matrices will be presented. A set of integrable ladder models based on this generalization of ABA will be formulated. The motivation for consideration of integrable models with staggered disposition of R-matrices comes from the phenomenological Chalker-Coddington (CC) model of edge excitations in quantum Hall effect, responsible for plateau-plateau transitions. We present the Action formulation of the CC model and average the Landauer resistance over U(1) phase disorder. It appears, that the resultant model is integrable since corresponding Yang-Baxter equations are satisfied.