This work presents a flexible type of origami structure that may be elastically deployed from a compact stacked form to a freeform target shape. The design process enables a target surface mesh to be converted into a compact stacked structure that may be deployed through the release of elastic energy stored in the folds. The process begins by finding a non-branching path passing once through each face in the target mesh. The edges of the target mesh not included in the path are cut and elastic smooth folds are introduced along those crossed by the path. The introduced smooth folds are folded in a sequence of ±180° along the path to create a stack. The structure transforms from the stacked form towards the target shape through the release of the stored elastic energy generated during stacking. The design framework considers the strain energy needed to sustain transformation and the required sizing of the smooth folds. The resemblance of the designed target shape with smooth folds compared to the target mesh is studied, and the significant volume saving when the structure is stowed in the stacked form is quantified. Examples showing the application of the design process to a diverse set of target meshes are provided. Proof-of-concept prototype fabrication using a 3D printer demonstrates the feasibility of the design approach. The results reflect the benefits of deployable stacked origami structures and show volumetric space savings from 50% to 90% while preserving around 80% of the target mesh area after the elastic smooth folds are introduced.