Recently, we have developed a multiscale soft matter cell model aiming at improving the understanding of mechanotransduction mechanism of stem cells, which is responsible for information exchange between cells and their extracellular environment. In this paper, we report the preliminary results of our research on multiscale modelling and simulation of soft contact and adhesion of stem cells. The proposed multiscale soft matter cell model may be used to model soft contact and adhesion between cells and their extracellular substrates. To the authors' best knowledge, this may be the first time that a soft matter model has been developed for cell contact and adhesion. Moreover, we have developed and implemented a Lagrange-type meshfree Galerkin formulation and related computational algorithms for the proposed cell model. Comparison study with experimental data has been conducted to validate the parameters of the cell model. By using the soft matter cell model, we have simulated the soft adhesive contact process between cells and extracellular substrates. The simulation shows that the cell can sense substrate elasticity by responding it in different manners from cell spreading to cell contact configuration and molecular conformation changes.