The disassembly is a fundamental basis in converting End-of-Life (EOL) products into useful components. Related research becomes popular recently due to the increasing awareness of environmental protection and energy conservation. Yet, there are many opening questions needed to be investigated, especially the efficient coordination of different-level decisions under uncertainty is a big challenge. In this paper, a novel integrated stochastic disassembly line balancing and planning problem is studied to minimise the system cost, where component yield ratios and demands are assumed to be uncertain. In this work, machine specificities are considered for task processing, such as price, ability, and capacity. For the problem, a two-stage non-linear stochastic programming model is first constructed. Then, it is further transformed into a linear formulation. Based on problem property analysis, a valid inequality is proposed to reduce the search space of optimal solutions. Finally, a sample average approximation (SAA) and an L-shaped algorithm are adopted to solve the problem. Numerical experiments on randomly generated instances demonstrate that the valid inequality can save around 11% of average computation time, and the L-shaped algorithm can save around 64% of average computation time compared with the SAA algorithm without a big sacrifice of the solution quality.