As a result of numerical modelling flat periodic fluid motions the decision of equation Navier-Stokes on the time interval amounting approximately 500÷2000 periods of natural time scale of flow, for R = 4000, α = 1,75; R = 5772, α = 1,25; R = 6000, α = 0,85 (precritical flow) and R = 5772, α = 1,025; R = 6000, α = 0,975; R = 6000, α = 1,020 (above-critical mode of flow) in the form of tables of Fourier factors, tables and images of lines of a flow. Perturbation in precritical modes of flow asymptotical aspired to zero. For above-critical modes by a method of an establishment are received quasi-periodical decisions in the form of a running wave. Period T for these modes appeared equal 2π / |Imλ₁|, where λ₁ is an eigenvalue of a linearized problem, having the maximal

material part.