As the required feature size of microelectronic devices continues to shrink, stringent process control of plasma etch process has become a critical issue in semiconductor manufacturing. In order to design a high-performance controller and its verification, there have been increasing needs for a high-fidelity model. This study proposes a probabilistic surrogate modeling method, named sparse Bayesian long short-term memory networks (SBLSTM). In SBLSTM, all the neural weights are given by parameterized Gaussian distributions, and the resulting distributional parameters are trained to maximize the posterior probability of the dataset. By imparting stochastic property to versatile neural network models, the proposed method allows modeling plasma etch processes’ complex behaviors. In order to find an optimal model structure, we propose a posteriori dropout, which eliminates insignificant weights after training based on their relative importance. The effectiveness of the proposed method is demonstrated through experimental data and compared with three conventional surrogate modeling techniques.