The paper analyses in details and describes the process of ignition kernel formation and subsequent detonation onset behind the shock wave propagating in the shock tube. To get the overall pattern of the process a series of one- and two-dimensional calculations are carried out with the use of a dissipation free numerical technique. It is shown that one of the leading roles in the process of ignition kernel formation belongs to the non-steady flow dynamics establishing behind the shock wave. The development of the boundary layer determines both the temperature re-distribution in the near-wall region and the conditions for gas-dynamic acceleration of the flow. With an account of thermal runaway, the most intensively heated region corresponds to the area between the inner margin of the boundary layer and the contact surface separating driver gas and the test mixture. After localized ignition takes place the forming reaction wave propagates out from the ignition epicenter. Reaction wave propagates behind the outrunning compression wave through the already reacting mixture. Shock-induced compression of the test mixture provides conditions for the self-sustained acceleration of the combustion wave, and finally, the detonation onset takes place. (C) 2019 The Combustion Institute. Published by Elsevier Inc. All rights reserved.