This paper presents tensor product formulas for modeling fault tolerant architectures and their corresponding reconfiguration algorithms. In our approaches, a network topology is first described with simple tensor product formulas, and then, by adding a set of permutation matrices and applying the direct sum operation, the reconfigurable architecture can be completely represented. Research results demonstrate three important facts: 1) by providing clarity and simplicity in mathematical form, tensor product representation is well-suited for the modeling of fault tolerant architectures; 2) with the tensor product model, traditional centralized reconfiguration processes can be transformed, in straightforward steps, to execute in a distributed manner; 3) furthermore, with the tensor product algebraic manipulations, complex architectures can be systematically and recursively constructed from simple basic blocks.