Capacity-approaching codes using iterative decoding have been the main subject of research activities during past decade. Especially, LDPC codes show the best asymptotic performance and density evolution has been used as a powerful technique to analyze and design good LDPC codes. In this paper, we apply density evolution with a Gaussian approximation to the concatenated zigzag (CZZ) codes by considering both flooding and two-way schedulings. Based on this density evolution analysis, the threshold values are computed for various CZZ codes and the optimal structure of CZZ codes for various code rates are obtained. Also, simulation results are provided to conform the analytical results.