The bound state spectrum of the low-lying triplet states in the Be atom is investigated. In particular, we perform accurate computations of the bound triplet S; P; D; F; G, H and I states in the Be atom. The results of these calculations are employed to draw the spectral diagram which contains the energy levels of the triplet states. Based on our computational results we can observe transitions from the low-lying bound states to the weakly-bound Rydberg states. For the 2(3)S; 3(3)S and 4(3)S states in the Be atom we also determine a number of bound states properties. Crown Copyright (C) 2014 Published by Elsevier B.V. All rights reserved.