Continuous adsorption in stirred reactors in the form of carbon in pulp (CIP) and resin in pulp (RIP) is an established process for the extraction of gold and uranium. Under the circumstance of intraparticle diffusion resistance, CIP and RIP have been accurately modeled by the Boyd's series (reversible adsorption) and shrinking core model (irreversible adsorption). The present study, in its first part, introduces an analytical formula that most closely approximates both models. Using such formula, the study addresses a basic algorithm for optimization of single-stage continuous adsorption systems through linking of the major process variables. Furthermore, this study is devoted to developing an "analytical kinetics approach" for the design of multistage CIP and RIP processes via application of Glauekauf's multiple series. Advantages of the new approach over the McCabe-Thiele "Equilibrium Approach" are (1) the incorporation of the kinetics and equilibrium into one unified model, and (2) accurate determination of the number of stages, reactor size, and optimum operational conditions.