Abstract: It is proposed in this paper that the fast tearing modes in cylindrical geometry is an effective heating mechanism for post-flare coronal arch of 21-22 May,1980 which have remained visible for more than 10 hours after the flare onset.The magnetic energy supplied by tearing modes,corresponding fast tearing modes grow the rate r_t and growth time r_t^-1 are calculated.The MHD equilibrium and stability of the arch are discussed.Main conclutions are as follows:(1)When density of the arch is given by the observational value,for different shearing width,the equilibrium can be made between radiative loss and tearing modes heating by taking different shearing magnetic field.But,in considering that corresponding tearing modes growth rate must be coincide with observation time,only one situation is reasonable.For coronal arch of 21-22 May,n_e=1.6×10⁹ cm,only shearing width a_a=1.8×10⁸cm(1/10 minal radius of the arch),shearing magnetic field B=18-32×10^-4T,r_t=1.79×10^-5-2.66×10^-5s^-1,r_t^{-1=15.5-10.4h,this solution is in agreement with observational value.The free energy which supplied by tearing modes can afford the radiative loss.So,fast tearing modes is an effective reasonable heating mechanism for the coronal arch.(2) According to the discussion for MHD equilibrium and stability of the arch,the arch which lasted more than 10 hours,must be in mechanical equilibrium besides the equilibrium between tearing modes heating and radiative loss.The equilibrium conditions are B_Ф (axis magnetic field of arch)=2B_θ(toroidal field intensity) and (dp/dr)>0.If the equilibrium conditions are satisfied,the arch is in stability for sausage,kink,screw perturbation by the energy principle.The axis magnetic field and toroidal field components can not be observed directly but an average pressure of 1.4 bar in the arch was observed,usually p_a (over the major active region)=2 bar.It can be thought that the arch of 12-22 May is in equilibrium condition and in a stable state.(3)According to observation and calculation for 21-22 May arch,when the tearing modes work,the thermal conduction in the coronal arch can be neglected.}