In this work we study the strain-induced deformation of both isotropic and anisotropic liquid droplets dispersed in a liquid crystalline cellulose matrix. We have produced two types of acetoxypropylcellulose (APC) solid films one with a droplet dispersion of the commercial liquid crystal E7 from Merck, and another with a droplet dispersion of silicone oil. To produce the solid films a solution of APC (60%wt) in dimethylacetamide (DMAc) with 15%wt of either the commercial nematic liquid crystal E7 or the silicone oil was prepared. After homogenization the phase separated solutions were submitted to a shear flow mechanical field and casted onto a Teflon plate. We performed mechanical uniaxial stress-strain tests in the free standing films recording continuously the strain and images of the deformed droplets. The mechanical tests were carried out using a mini stress-strain testing machine apparatus and an Olympus optical polarizing microscope with an attached CCD camera. The images obtained from the mechanical tests for each value of the imposed strain were then analyzed comparing the images of deformed droplets with those of the undeformed ones, extracting in this way the local strain field. The droplet deformation data obtained show, as expected, significant differences in the local strain field when stretching parallel and perpendicular to the initial shear direction. No significant differences were found in the local strain fields obtained from the silicone oil and the E7 droplets films. The local strain fields variation with the imposed strain are compared with the predictions of the theory developed for nematic elastomers by Warner and Terentjev (Liquid crystal elastomers.