For a class of stochastic cellular neural networks with discrete delays and impu-lses (SDCNNswI), this paper discusses their exponential stability and the existence of periodic solutions. Firstly, Poincare contraction theory is utilized to derive the conditions to guarantee the existence of periodic solutions of SDCNNswI. Next, Lyapunov function, stochastic analysis theory and Young inequality are develo-ped to derive some theorems. These theorems provide several sufficient conditions to guarantee that the periodic solutions of SDCNNswI are mean square exponentially stable. These sufficient conditions only include the governing parameters of SDCNNswI and can be easily checked by simple algebraic methods. Finally, two examples are given to demonstrate the usefulness of the obtained results.