Thunderstorm downbursts are responsible for numerous structural failures around the world. The wind characteristics in thunderstorm downbursts containing vortex rings differ with those in 'traditional' boundary layer winds (BLW). This paper initially performs an unsteady-state simulation of the flow structure in a downburst (modelled as a impinging jet with its diameter being Djet) using a computational fluid dynamics (CFD) method, and then analyses the pressure distribution on a solar updraft tower (SUT) in the downburst. The pressure field shows agreement with other previous studies. An additional pair of low-pressure region and high-pressure region is observed due to a second vortex ring, besides a foregoing pair caused by a primary vortex ring. The evolutions of pressure coefficients at five orientations of two representative heights of the SUT in the downburst with time are investigated. Results show that pressure distribution changes over a wide range when the vortices are close to the SUT. Furthermore, the fluctuations of external static pressure distribution for the SUT case 1 (i.e., radial distance from a location to jet center x=Djet) with height are more intense due to the down striking of the vortex flow compared to those for the SUT case 2 (x=2Djet). The static wind loads at heights z/H higher than 0.3 will be negligible when the vortex ring is far away from the SUT. The inverted wind load cases will occur when vortex is passing through the SUT except on the side faces. This can induce complex dynamic response of the SUT.