Cell deformability is a useful feature for diagnosing various diseases (e.g., the invasiveness of cancer cells). Existing methods commonly inflict pressure on cells and observe changes in cell areas, diameters, or thickness according to the degree of pressure. Then, the Young’s moduli (i.e., a measure of deformability) of cells are estimated based on the assumption that the degrees of the changes are inversely proportional to Young’s moduli. However, manual measurements of the physical changes in cells are labor-intensive, and the subjectivity of the operators can intervene during this step, thereby causing considerable uncertainty. Further, because the shapes of cells are nonuniform, we cannot ensure the assumption for linear correlations of physical changes in cells with their deformability. Therefore, this study aims at measuring non-linear elastic moduli of live cells (degrees of cell deformability) automatically by employing conventional neural networks (CNN) and multilayer perceptrons (MLP) while preserving (or enhancing) the accuracy of the manual methods. First, we obtain photomicrographs of cells on multiple pressure levels using single-beam acoustic tweezers, and then, we suggest an image preprocessing method for emphasizing changes in cell areas on the photomicrographs. The CNN model is trained to measure the ratios of the cell area change at each pressure level. Then, we apply the multilayer perceptron (MLP) to learn the correlations of the cell area change ratios according to the pressure levels with cell deformability. The accuracy of the CNN was evaluated using two types of breast cancer cells: MDA-MB-231 (invasive) and MCF-7 (noninvasive). The MLP was assessed using five different beads (Young’s moduli from 0.214 to 9.235 kPa), which provides standardized reference data of the non-linear elastic moduli of live cells. Finally, we validated the practicality of the proposed system by examining whether the non-linear elastic moduli estimated by the proposed system can distinguish invasive breast cancer cells from noninvasive ones.