Shape deformation of polymeric droplets on gel-like surfaces is studied by using a combination of the molecular dynamics simulations and theoretical calculations. On the basis of the results of molecular dynamics simulations, we have developed a theoretical model of droplet shape deformation on elastic surfaces which takes into account surface and elastic energy contributions. Analysis of simulation results in the framework of this model shows that the equilibrium droplet shape is controlled by the dimensionless parameter gamma(SL)/G(S)a, where gamma(SL) is the surface tension of the substrate/liquid interface, G(S) is the shear modulus of the substrate, and a is the contact radius of polymeric droplet. This parameter describes crossover between Neumanns triangle conditions for liquid droplets on liquid substrates and Youngs law for droplets on rigid substrates. In the limit when the elastocapillary length is much larger than the contact radius, gamma(SL)/G(S) >> a, we recover the Neumanns triangle conditions for liquid droplets floating on liquid substrates. However, in the opposite limit, gamma(SL)/G(S) << a, our model reproduces Youngs law. The model predictions are in a very good agreement with simulation results and experimental data.