Smooth functions can be represented with isogeometric discretization effectively. Discontin- uous functions, however, may not be represented as effectively. T-splines provide effective refinement without subdividing where we do not need higher mesh resolution, and we apply the “product-form” T-splines [1] to track the shock waves. With the product-form T-splines, functions are represented by the product of basis functions defined individually in each parametric direction. They are efficient, especially in higher dimensions, because derivatives can be evaluated by multiplication of 1D basis functions. We propose a T-splines adaptive mesh refinement (AMR) strategy for capturing the shock waves. The strategy has two key features: 1. Representation of the basis functions. Each basis function is represented with Bézier-extraction row operators [1], which enable compact data storage and simplify the mesh refinement process. 2. Identification of the element structure. In the product-form T-splines, the 1D basis functions for each direction are calculated from the local knot spans. We determine the knot spans by identifying the element structure that the split basis functions have support in. In this process, we need only the information about the elements supporting each global basis function. Therefore, the refinement process can be done automatically, even in meshes for complex geometries. The T-splines AMR is applied to test problems where the shock waves are computed with the compressible-flow Space–Time SUPG method [2], and the element-length calculation is from [3].