This paper presents the kinematic modeling and design of deployable structures inspired by pop-up books. These pop-up structures can exhibit large changes in area and volume through deployment motion that resembles opening the pages of a book. The pop-up structures have a modular topology and are formed by multiple parallelepiped units, here termed as pop-up units. The analysis of the kinematics of single pop-up units and assemblies of these that form larger structures is presented. An algorithm that integrates multiple pop-up units to form structures that approximate two-dimensional and three-dimensional target shapes when deployed is subsequently devised. The algorithm ensures that the structures formed by the assemblies of multiple pop-up units retain the single degree of freedom of a pop-up unit. The stored strain energy of these structures, which can provide the means to deploy them in practice, is also analyzed. Finally, various examples showing the applicability of the design algorithm in the synthesis of pop-up structures that approximate a diverse set of two-dimensional and three-dimensional target shapes are provided. The pop-up structures can be applied to a large spectrum of applications that need extensive deployment from small volumes while requiring a low number of degrees of freedom. These applications may include aerospace structures and MEMS.

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