The dynamics of two model glass-formers (3D oligomer melt and 2D polydisperse colloidal system) are analyzed using MD simulations. It is found that the standard deviation of the shear modulus shows a striking peak near the glass transition T g , which is explained with a quantitative theory. The simulation data well below T g suggest that static multi-point correlations of local stress are long-range. The obtained correlation functions of time-dependent and wavevector-resolved stress for the 2D system are in excellent agreement with the developed theory indicating that the frozen-in stress inhomogeneities in the glassy state are correlated according to a power law.