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Abstract Trapping of strain in layers deposited during extrusion‐based (fused filament fabrication) 3D printing has previously been documented. If fiber‐level strain trapping can be understood sufficiently and controlled, 3D shape‐memory polymer parts could be simultaneously fabricated and programmed via printing (programming via printing; PvP), thereby achieving precisely controlled 3D‐to‐3D transformations of complex part geometries. Yet, because previous studies have only examined strain trapping in solid printed parts—such as layers or 3D objects with 100% infill—fundamental aspects of the PvP process and the potential for PvP to be applied to printing of porous 3D parts remain poorly understood. This work examines the extent to which strain can be trapped in individual fibers and in fibers that span negative space and the extent to which infill geometry affects the magnitude and recovery of strain trapped in porous PvP‐fabricated 3D parts. Additionally, multiaxial shape change of porous PvP‐fabricated 3D parts are for the first time studied, modeled, and applied in a proof‐of‐concept application. This work demonstrates the feasibility of strain trapping in individual fibers in 1D, 2D, and 3D PvP‐fabricated parts and illustrates the potential for PvP to provide new strategies to address unmet needs in biomedical and other fields.