Context. Flaring coronal loops are often observed in microwave and sometimes in soft X-rays, as extended structures of variable cross-section or width. The quasi-periodic pulsations associated with flaring coronal loops have been interpreted in terms of standing, fast sausage magnetoacoustic modes and suggested for the diagnostics of the magnetic field outside the oscillating loop.Aims. We investigate the effects of a non-uniform cross-section on a coronal loop with respect to the standing sausage modes it supports.Methods. Numerical simulations of standing sausage modes are performed for a straight, zero-$β$ coronal loop with a varying cross-section. The global sausage mode and higher harmonics are considered, and simulations were performed for a range of density contrast ratios and loop divergence parameter. We consider modifications of the period of oscillation and the spatial profile of the standing modes.Results. As the loop divergence parameter increases, the period of the standing modes decreases. The fractional change period is independent of the density contrast ratio. The spatial profiles of the standing modes are modified by the cross-section inhomogeneity, but this effect is too weak to be observable by modern instruments. For the global sausage mode, the cross-section radius divergence by a factor of 2 is found to cause the decrease in the period of about 5%.