Mechanical response of DT targets to acceleration was analyzed using the finite element method for Inertial Fusion Energy (IFE) targets and for smaller targets that have been proposed for an upcoming Fusion Test Facility (FTF). Analysis was done in the temperature and acceleration regions of interest for Inertial Fusion Energy (14-19 K and 1,000-10,000 m/s2). In these ranges, von Mises stress distribution, axial deflection, and the minimum value of support membrane attachment angle as well as free vibrations of the target after it leaves the injector were calculated. The role of the outer polymer coating, the support membrane attachment angle and the DT void pressure in the mechanical response of a DT target to acceleration was considered. Analysis shows, assuming that DT mechanical properties are equivalent to D2, that IFE and FTF targets should withstand acceleration of up to 10,000 m/s2 with negligible deformation.