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To investigate the migration response of cells to changes in their biophysical environment, a novel uniaxial cell stimulation device (UCSD) has been designed and tested. The device is capable of applying very precise user-defined static or dynamic mechanical stimuli in a physiologically relevant strain window (up to 50%) and frequency bandwidth (up to 2Hz) to cells residing in a three-dimensional (3D) environment while single-cell migration is simultaneously measured by time-lapse microscopy. The system is an advancement over uniaxial loading devices reported to date in that it allows temporal and spatial quantification of migration as a function of the micromechanical environment. We make use of the favorable physical and biological properties of poly(ethylene glycol) hydrogels as model matrix and present a method for fabricating cell-containing hydrogel constructs. The 3D strain field within these constructs is modeled by finite element analysis. Fibroblasts reversibly altered their morphology and orientation in response to the strain field. In the succeeding companion paper we then exploit the system to analyze fibroblast motility induced by different stimulation regimes (refer to part II).