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We present the dynamics of the kinetically constrained Ising model, comprised of a system of spins coupled with the strength J and situated in a field which plays the role of activation energy. Due to kinetic constraints, glassy effects arise at low temperatures leading to a non-Arrhenius α -relaxation time. The results of Monte Carlo simulations are presented for the 2D and 3D facilitated kinetic Ising model with nonzero coupling J. The spin autocorrelation function exhibits, in a broad intermediate time regime, a pronounced stretched exponential decay characterized by an exponent γ . Whereas the relaxation time depends strongly on the activation energy and the interaction strength J, we find a non-universal stretching exponent γ depending on the temperature and on J. In 3D the autocorrelation function shows a crossover into a pure exponential decay consistent with theoretical predictions. The magnetization is also analyzed and identified as a control parameter of the system.