Abstract: This paper studies the stochastic power multi-coverage problem: Given some users and base stations, as well as several possible scenarios and the probability of each scenario occurring, the users that need to be covered and the coverage times required in each scenario are known. Different signal coverages are needed for the user sets in different scenarios. The power consumed by each base station transmitting signal satisfies the power equation. The objective of the stochastic power multi-coverage problem is to determine the type of signal and its coverage radius for each base station, which meet the coverage times required for the users needing to be covered in all scenarios, and minimize the total expected power consumption. This problem is a generalization of the minimum power coverage problem and has the characteristic of finite scenarios in two-stage stochastic optimization problems, closely related to classical optimization problems such as vertex cover and set cover. By using the “degree-weighted” function and “layering” strategy from the vertex cover and the set cover problems, we decompose the weight of each disk in the problem instance into a series of degree weights, and prioritize the selection of disks with smaller degree weights in each scenario. Using this strategy, we design a polynomial-time approximation algorithm for solving the stochastic power multi-coverage problem.