An expression is obtained for the resistance force of fractal objects (fractal aggregates, fractal tangles, aerogels) that are moving in a gas. A fractal object is consisdered as a system of independent balls with a radius which is small compared with the free path length of gaseous molecules. The expression for the mobility of fractal aggregates is obtained. It is shown the validity of the Gaidukov statement that a viscosity layer absents on the boundary of a fractal object and gas. Penetrating of a gas inside fractal objects is analyzed.