We have studied a GaAs/AlAs quantum dot array using reciprocal space mapping around the (004) and (II3) reciprocal lattice points. Both the coherently and the diffusely scattered X-ray intensities were analysed by performing two-dimensional model calculations. From the distribution of the diffracted intensities we deduced the average strain status in the dots. From the numerical simulations it is evident that random elastic strain fields are present, which extend through almost the whole volume of the quantum dot. The simulations of the X-ray measurements revealed that the crystalline part of the dots is considerably smaller as scanning electron micrographs would indicate, namely 50 nm instead of 65 nm, respectively.