This thesis is on fluid and structural mechanics computation of spacecraft parachutes based on isogeometric discretization with T-splines. Contrary to the non-uniform rational B-splines (NURBS), T-spline representation does not require a regular control grid, allowing a set of control points to end without traversing the whole domain. We generate a T-spline mesh directly from a block-structured NURBS mesh. In T-spline representation, we use knot removal at the unnecessarily refined regions of the NURBS mesh and reduce the number of control points. We use knot insertion at interfaces between nonmatching meshes. Then, having the matching pairs of control points on each side of the interface, we use knot removal to remove the other knots on the interface sides and enhance the continuity in the whole domain. This gives continuity, or increased continuity, to the volume mesh, improving the solution accuracy and reducing the total number of unknowns compared to NURBS computations. We first present, for a 2D parachute model, fluid--structure interaction computation based on the Space--Time Isogeometric Analysis (ST-IGA) with NURBS and T-splines. Then, we present spacecraft parachute incompressible- and compressible-flow computations based on the ST-IGA with T-splines.