Assessment of mechanical properties of soft matter is a challenging task in a purely noninvasive and noncontact environment. As tissue mechanical properties play a vital role in determining tissue health status, such noninvasive methods offer great potential in framing large-scale medical screening strategies. The digital speckle pattern interferometry (DSPI)–based image capture and analysis system described here is capable of extracting the deformation information from a single acquired fringe pattern. Such a method of analysis would be required in the case of the highly dynamic nature of speckle patterns derived from soft tissues while applying mechanical compression. Soft phantoms mimicking breast tissue optical and mechanical properties were fabricated and tested in the DSPI out of plane configuration set up. Hilbert transform (HT)-based image analysis algorithm was developed to extract the phase and corresponding deformation of the sample from a single acquired fringe pattern. The experimental fringe contours were found to correlate with numerically simulated deformation patterns of the sample using Abaqus finite element analysis software. The extracted deformation from the experimental fringe pattern using the HT-based algorithm is compared with the deformation value obtained using numerical simulation under similar conditions of loading and the results are found to correlate with an average %error of 10. The proposed method is applied on breast phantoms fabricated with included subsurface anomaly mimicking cancerous tissue and the results are analyzed.