Previous computational investigations of shock initiation of detonable substances have demonstrated the utility of numerical (high-speed computer) methods in furthering the understanding of the initiation and detonation behavior of materials in the condensed state. The previous investigations were all one-dimensional studies, except for Mader's work. Mader has carried out two-dimensional computational studies showing the effect of a single inhomogeneity upon the development of detonation. However, up to the time of this work, no published material has been found which employs such computational methods to study the transient process of shock initiation of detonation in cylindrical charges, and to predict the critical diameter of a homogeneous explosive. In this study, the transient initiation process for unconfined nitromethane is studied as a function of charge diameter. For subcritical charge diameters, the initial reactive shocks eventually decay to a nonreactive shock. For a sufficiently large diameter, steady-state propagation is attained. This defines the critical diameter. Computations of the detonation behavior resulting from shock initiation are performed by means of the SHEP program, which makes possible the simultaneous numerical solution of the fundamental differential conservation equations together with the chemical reaction-rate equation and the equation of state. The SHEP program is based on a Lagrangian formulation employing a convective coordinate system which moves and distorts with the material. As a computational simplification, the Enig-Petrone equation of state for nitromethane (based on work of Walsh and Christian) was used for both the reacted as well as the unreacted nitromethane. Computations of shock initiation of unconfined, chemically reactive nitromethane cylinders of 5, 10, 12, 15, 20, 25, and 30 mm diameter were performed, with an impacting aluminum plate providing an 88 kbar shock of about 1.1 μsec duration. All diameters less than 30 mm yielded results showing initial energy release and a partial buildup toward detonation, followed by a fadeout of the reaction process. The 30-mm-diameter case furnished results indicating that a steady-state condition has been reached. This computed value of the critical diameter for unconfined nitromethane is in unexpectedly good agreement with the experimental value for paper confined nitromethane ranging from 26.5 to 29 mm, as determined by Nachmani and Manheimer. Agreement between computed (0.5 μsec) induction times and an average experimental value (1.7 μsec) reported by Campbell, Davis, and Travis is not as good. The computations yield a detonation velocity of 0.63 cm/μsec, whereas measured values range between 0.615 and 0.628 cm/μsec. The peak shock pressure in the compressed, unreacted nitromethane derived from the computations (290 kbar) is in reasonable agreement with the experimental value (300 kbar) cited by Mader. The cell dimensions used in this investigation (0.05×0.05 cm) were too large to resolve the steady-state reaction zone for nitromethane. Nevertheless, there is observable resolution of the transient reaction zone especially near the cylinder edges where the pressures and the reaction rates are low.