Mechanical property of biological cells can act as an indicator for the health state of a human being. Mathematical modelling of cells help to understand and predict the cell deformation patterns that might provide insightful finding for cell mechanics. Many models have been developed that tries to explain the cell mechanics at the cellular level. We propose an analytical model that considers the poroelastic nature of cells to understand their deformation behavior. The validity of the model is tested by comparing the predicted cell deformations against the experimental observations reported by Raj et al. (2017). Also, a computational study is performed, where we employ an in house Python code along with MS Excel GRG solver which incorporates the cell deformation predictions from developed poroelastic model and predicts the Young’s modulus value of the cells. The predictions using GRG based approach showed a good match with the experimental results with a maximum error of 12.09% in the case of MDA MB-231 cells. Further, we present an artificial neural network model to predict the Young’s modulus and viscosity of cells based on the experimentally measured input parameters such as entry time, transit velocity, initial cell diameter and extension ratio from the cell migration process through a micro-constriction channel. It was found that the neural network with architecture of 4-5-1 was best suited for the MCF-10A cells while the 4-8-1 architecture was giving better results for the MDA MB-231 cells. The developed ANN model is further tested for Young’s Modulus prediction of HeLa cells with completely new set of data. The predictions from ANN based model for HeLa cells matched well the experimental prediction within 4.5 % of error.