**Abstract:** We will establish that the discrete spectrum of Dirichlet Laplacian in the union of two orthogonal circular cylinders has total multiplicity one. Also we are going to discuss the same problem concerning other shapes of cross-section. In particular it is proved that the multiplicity of the discreet spectrum depends on the shape of cross-section, and on the value of the angle between cylinders as well. In addition we prove that the homogeneous problem at the threshold of the spectrum has no bounded solutions. This information provides to give a one-dimensional model of a square lattice of thin quantum waveguides and to describe the asymptotic behaviour of spectral segments and gaps.