This research performs a surrogate-assisted shape optimisation of hypersonic waveriders, where the trajectories of each shape are optimised with a multi-objective evolutionary algorithm for heat-load and cross-range. A study on the best evolutionary algorithm, node control strategy for angle of attack and bank angle profiles, and population size to use in the trajectory optimisation phase, are identified. The aerodynamics of the waveriders is computed with a new local surface inclination method blending the modified Newtonian and tangent wedge solutions, while the convective heat flux is computed for the leading edges using the Newton-Kays engineering model. Shape variability is introduced according to the layout of central composite designs, and analysis of variance is applied to identify the shape features driving the two objectives. Shock angle, leading edge radius and overall vehicle dimensions are the strongest drivers, while details on the planform shape are less relevant and should be left for posterior studies. The surrogates are a good approximation of the true fitness functions, so they were optimised in a single-objective framework, producing two optimal waverider designs.