Cross approximation in tensor electron density computations The paper studies approximations of a discrete electron density function (and its cubic root) related with the Hartree-Fock/Kohn-Sham equation. To be able to realize the computations for large scale problems, it is necessary to find a suitable structured approximation to such functions. First, it is assumed that a function is discretized on a tensor grid giving a tensor in the canonical format. Classical algorithms for computing Tucker and cross approximations of such tensors are compared with a new algorithm based on cross2D approximations. Then, approximations to a general form tensors are discussed. Storage and computational cost of all algorithms are compared. It is shown that the new algorithm is superior especially for tensors in the canonical or smooth elementwise canonical form.