[en] We combine atomistic calculations and continuum laws to model irradiation-induced vacancy and interstitial dislocation loops in $\alpha$-zirconium. A comprehensive set of Burgers vectors/stacking sequences in the prismatic and basal planes, of sizes accessible to experiments, are studied by Molecular Statics (MS) simulations. Their formation energies and structural details are determined using two different interatomic potentials for $\alpha$-Zr, considering dislocation loops in hexagonal and circular shapes. Molecular Dynamics annealing of dislocation loops then validates the envisioned potential energy landscape. Finally, the continuum modelling hybridly calibrated on MS results and ab initio data indicate that the coexistence of vacancy and interstitial $〈a〉$ loops is supported by stability arguments. We also establish the limitations of such an approach for quantitative predictions.