We study the conveyor sortation system from performance evaluation and design perspectives employing continuous modeling approach. We present two continuous conveyor models with different level of accurary in a uniform mathematical framework. We study the accurarcy difference of these two representations and give rationales of generating this difference. We also conduct rigorous sensitivity analysis on these two models which lays the foundation to utilize them in optimization applications. Based on the Batch on conveyor Model, we develop a fast fluid simulation methogology. We address the feasibility of implementing fluid simulation from modeling capacilities , algorithm design and simulation performance in terms of accuracy and simulation time. From design perspective, we focus on rates determination and accumulation design in the accumulation and merge subsystem. The optimization problem is to find a minimum cost design that satisfies some predefined performance requirements under stochastic work environment. We first transfer this stochastic programming problem to a deterministic nonlinear programming problem through sample path based optimization method. Gradient based method is adopted to solve the deterministic problem. Since there is no close form for performance metric even for a deterministic input stream, we adopt continuous modeling to develop deterministic performance evaluation models and conduct sensitivity analysis on these models. We explore the prospects of using two continuous conveyor models we presented. We perform numerical experiments on a two conveyor segment tandem system which is the building block of more complex network.