The resistance distance between any two vertices of a connected graph is defined as the effective resistance between them in the electrical network constructed from the graph by replacing each edge with a unit resistor. The Kirchhoff index of a graph is defined as the sum of all the resistance distances between any pair of vertices of the graph. Let G = H[G(1), G(2),., G(k)] be the generalised join graph of G(1), G(2), ..., G(k) determined by H. In this paper, we first give formulae for resistance distances and Kirchhoff index of G in terms of parameters of G(i)'s and H. Then, we show that computing resistance distances and Kirchhoff index of G can be decomposed into simpler ones. Finally, we obtain explicit formulae for resistance distances and Kirchhoff index of G when G(i)'s and H take some special graphs, such as the complete graph, the path, and the cycle.