The atomic structure of pure amorphous Re and Re-Tb amorphous alloys was studied by the molecular dynamics method. Analysis of the atomic structure of amorphous metals was performed within the framework of percolation theory and fractal geometry. The structure of amorphous metals consists of dense and sparse areas. We established that the dense areas form the fractal skeleton of an amorphous material. The distribution of clusters by size, the probability of an atom belonging to the largest cluster, the fractal dimensionality of the percolation cluster and the concentration dependence of the percolation radius were calculated. Correlation between some physical properties of amorphous metals and their cluster structure was established.