Abstract. We study fast sausage waves in a model coronal loop that consists of a cylindrical core with axial magnetic field and coaxial annulus with purely azimuthal magnetic field. The magnetic field is discontinuous at the tube and core boundaries, and there are surface currents with the opposite directions on these boundaries. The principal mode of fast sausage waves in which the magnetic pressure perturbation has no nodes in the radial direction can exist for arbitrary wavelength. The results for the fundamental radial mode of sausage waves are applied to the interpretation of observed periodic pulsations of microwave emission in flaring loops with periods of a few tens of seconds. Radial plasma motion has opposite directions at the tube and core boundaries. This leads to the periodic contraction and expansion of the annulus. We assume that the principal mode of fast sausage waves in the current-carrying coronal loops is able to produce a current sheet. However, the nonlinear analysis is needed to confirm this conjecture.