Detonation is a combustion-driven supersonic shock wave that can reach speeds of several kilometers per second. Applications range widely, from jet propulsion to the theory of supernova explosions. In our work we investigate the linear stability and receptivity of the Zel'dovich-von Neumann-Doering (ZND) detonation wave model. The solution of the initial-value problem for small three-dimensional perturbations in a ZND detonation is presented as an expansion into modes of discrete and continuous spectra. The result provides a tool to predict initial amplitudes of the unstable modes depending on the initial perturbation. The results for different types of introduced perturbations are discussed.