Let \( G \) be an undirected simple graph with \( n \) vertices and let \( d_i \) be the degree of the vertex \( i \) in \( G. \) The \( ABC \) matrix of \( G \) is a square matrix of order \( n \) whose \( (i,j) \)- entry is \( \sqrt{\frac{d_i+d_j-2}{d_id_j}}, \) if the vertices \( v_i \) and \( v_j \) are connected and zero otherwise. Let \( H \) be a simple undirected graph with \( r \) vertices, \( v_{1},v_{2},\ldots ,v_{r} \) and \( G_{1}, G_{2}, \ldots ,G_{r} \),\ \( r \) disjoint \( p_j \)- regular graphs, \( j = 1, \ldots, r \). The \( H \)-join of \( G_{1}, G_{2}, \ldots ,G_{r}, \) denoted by \( H[G_{1},G_{2},\ldots ,G_{r}], \) is the graph \( G \) obtained by joining each vertex of \( G_{i} \) to all vertices of \( G_{j} \) whenever the vertices \thinspace \( v_{i} \) and \( v_{j} \) are neighbors in \( H \) for all \( 1\leq i,j\leq r \). In this work, the \( ABC \) spectrum, the \( ABC \) spectral radius, and the \( ABC \) energy of certain caterpillars trees are studied.