Market players face electricity market price uncertainty as a challenging issue in restructured electricity markets. To overcome this problem, taking optimal bidding and offering strategies is very important. This paper proposes a new mathematical model as a hybrid robust-stochastic method in order to maximize the expected profit of a compressed air energy system. Also, this study considers the uncertainty of market price with a set of scenarios via stochastic method while it models the uncertainty of maximum capacity of cavern via robust optimization approach. Furthermore, the proposed model formulates mixed-integer linear programming and obtains optimal offering and bidding curves of a compressed air energy system, which are robust against the uncertainty associated with market price and cavern uncertainty. Obtained results show that total profit, without considering cavern's uncertainty, is equal to $9585 while this amount for the most robust case obtained as $8753. This means that being robust against the maximum capacity of caver's uncertainty reduces total profit by about 8.68%. (C) 2019 Elsevier Ltd. All rights reserved.