We present three dimensional smoothed particle hydrodynamics ( SPH ) calculations of warped accretion discs in X-ray binary systems . Geometrically thin , optically thick accretion discs are illuminated by a central radiation source . This illumination exerts a non-axisymmetric radiation pressure on the surface of the disc resulting in a torque that acts on the disc to induce a twist or warp . Initially planar discs are unstable to warping driven by the radiation torque and in general the warps also precess in a retrograde direction relative to the orbital flow . We simulate a number of X-ray binary systems which have different mass ratios using a number of different luminosities for each . Radiation-driven warping occurs for all systems simulated . For mass ratios q \sim 0.1 a moderate warp occurs in the inner disc while the outer disc remains in the orbital plane ( c.f . X \thinspace 1916 - 053 ) . For less extreme mass ratios the entire disc tilts out of the orbital plane ( c.f . Her X-1 ) . For discs that are tilted out of the orbital plane in which the outer edge material of the disc is precessing in a prograde direction we obtain both positive and negative superhumps simultaneously in the dissipation light curve ( c.f . V603 Aql ) .