In this paper, a mathematical model is developed to estimate specifications of a clamp band joint by taking into account full effects of the uncertainty of the joint parameters with a reasonable amount of computational cost. In the model, the clamp band joint is partitioned into sectors which are substituted with equivalent springs. The mathematical formulation of the stiffness and load bearing capacity of the joint is derived under combination of the loads. Nonlinear finite-element analysis is conducted to verify the proposed formulation, where all parameters have their nominal value. Finally, a procedure is introduced, in which one can specify the uncertainty of the joint parameters and the safety factor to obtain a desired reliability level from a table.