The problem of the minimum run-up distance for the flame acceleration to supersonic combustion regimes in tubes with obstacles is studied both experimentally and numerically. Experiments were made in an explosion tube equipped with orifice plate obstacles. The tube was of 12-m long with internal tube diameter of 0.35 in. Blockage ratios (BR) of the orifice plates were 0.3, 0.45, 0.6 and 0.75. Hydrogen mixtures were used in the tests. The process of the flame acceleration in a geometry, which is similar to the experimental one, was studied numerically in a series of 3D gasdynamic simulations. It was found both in the tests and in the simulations that characteristic distance of the flame acceleration decreases with the increase of the blockage ratio and with the increase of the mixture reactivity (burning rate). A simple analytical model is proposed, which describes the evolution of the flame shape in the channel with obstacles. The dimensionless flame acceleration distance is determined in the model, which accounts for BR, laminar burning rate, and sound speed in combustion products.