<1>¿¿MHD-oscillations of an inhomogeneous coronal loop consisting of a dense cord and a surrounding shell are investigated. Magnetic field in the cord is longitudinal and in the shell is azimuthal only. Usually the nonuniform field leads to the existence of resonance. However here we assume the resonance points non exist in the tube, i.e. the resonances are cutted. Our approach pursue a target - an investigation of an influence of the wave radiation on the tube oscillations. The resonant absorption of tube oscillation energy is eliminated. The same tube effectively radiate a magnetosonic waves into the environment and the Q-factor of the tube oscillations is small. The presented model can explain the fast damping of the coronal loop oscillations observed by the TRACE EUV channel.