Cosmic rays hitting the outer parts of the Sun result in showers of high energy particles. The shower particles propagate through the solar atmosphere and interact further or decay. Among the shower particles are high energy neutrinos, after production these oscillate between flavours and interact with the solar material while propagating out of the Sun to the Earth. The result is a high energy neutrino flux at the Earth that may be detectable by modern neutrino detectors such as IceCube. Such a neutrino flux will furthermore act as a background in searches for neutrinos coming from annihilations of weakly interacting massive particles, often suggested to be the dark matter in the Universe. We perform an updated calculation of the solar atmospheric neutrino flux using the code MCEq for the cascade evolution in the solar atmosphere and WimpSim for the propagation of the neutrinos from the Sun to the detector on Earth, including full three-flavour treatment of neutrino oscillations and interactions in the Sun.