We investigate a topology optimisation based on the level set method for a design problem of carpet cloaking devices. In topology optimisation of carpet cloaking devices, we need to calculate the electromagnetic response in a semi-infinite domain. We use the boundary element method (BEM) for the electromagnetic analysis since the BEM is more suitable to topology optimisation in wave field than the finite element method; the infinite domain can be evaluated exactly and mesh generation is required only on a boundary with the BEM. Along with the detailed formulation of the BEM-based topology optimisation, we present some numerical examples of design for carpet cloaks. We have confirmed that the designed carpet cloaking devices effectively work for the cases where permittivity, wavelength and angle of incidence are fixed. In addition, we have confirmed that cloaking devices for perturbed permittivity and wavelength can be obtained by redefining the objective function with the KS function.