We measured Raman spectra of free-standing polycrystalline films of 3C-Sic as a function of the tunable biaxial strain in micromachined diaphragms. The results are used to determine the Raman stress coefficients eta (TO,LO)(S) for uniaxial stress along the [100]-axis. From the stress induced shifts of TO- and LO-phonon frequencies the residual strain in 3C-SiC layers on Si(100) are determined as a function of the layer thicknesses. Largest tensile stress is found in thin films; it relaxes for thicker films to a value imposed by the different thermal expansion coefficients of SiC and Si. Accompanying the strain relaxation we observe a narrowing of the Raman lines that indicate an improved crystalline quality.