The integral equations for DC conductivity and external conductance for the network of localised states in amorphous solids are solved by iteration method. The random free energy barriers and single polaron hoppingmodel are used to obtain the DC conductivity $\sigma_\rm{DC}$ and Meyer–Neldel energy $E_\rm{MN}$. The experimental estimates of optical band gap $E_\rm{g}$, dielectric function $\epsilon$, glass transition temperature $T_\rm{g}$ and $\sigma_\rm{DC}$ are used to calculate $E_\rm{MN}$ for Se-based binary and ternary chalcogenide glasses. The calculated values are found to be in agreement with the available experimental data. $E_\rm{MN}$ increases with increase of attempt frequency. The true pre-exponential factor $\sigma_\rm{00}$ is related to $E_\rm{MN}$ as ln $\sigma_\rm{00} = p − q E_\rm{MN}$, where $p$ is nearly 7.3 and $q$ is material-dependent. The calculated values of $E_\rm{MN}$ and $\sigma_\rm{00}$ suggest that DC conduction in these chalcogenides is due to acoustic and optical phonon-assisted polaron hopping.