The linear canonical Stockwell transform (LCST) is an extension of the Stockwell transform (ST) and the linear canonical Fourier transform (LCT). It not only characterizes signals in the time-linear canonical frequency plane but also inherits the advantages of the Stockwell transform. This study aims to generalize LCST into a two-dimensional linear canonical Stockwell transform (2D LCST) in response to the widespread interest in 2D ST across various fields.We begin by examining the fundamental aspects of the two-dimensional linear canonical Stockwell transform, including its definition, basic properties, and Parseval formula. Subsequently, we introduce and investigate a comprehensive reconstruction formula and an energy formula. As we approach the conclusion, we derive the convolution theorem and the cross-correlation theorem associated with the two-dimensional linear canonical Stockwell transform.