The ground state energy of hydrogen molecular ion [H.sup.+.sub.2] confined by a hard prolate spheroidal cavity is calculated. The case in which the nuclear positions are clamped at the foci is considered. Our calculations are based on using the variational Monte Carlo method with an accurate trial wave function depending on many variational parameters. The results were extended to also include the He[H.sup.++] molecular ion. The obtained results are in good agreement with the most recent results. Key words: variational methods, Monte Carlo methods, molecular structure, ground state of [H.sup.+.sub.2] and He[H.sup.++] confined quantum systems. Nous calculons l'energie du fondamental de l'ion d'hydrogene moleculaire [H.sup.+.sub.2] confine dans une cavite spheroide oblong. Nous considerons le cas ou les positions nucleaires sont fixees aux foyers. Nos calculs sont bases sur une methode Monte Carlo variationnelle, avec une fonction d'onde precise dependant de plusieurs parametres variationnels. Nous etendons nos calculs au cas de l'ion moleculaire He[H.sup.++]. Les resultats obtenus sont en bon accord avec les plus recents resultats. [Traduit par la Redaction] Mots-cles: methodes variationnelles, methodes de Monte Carlo, structure moleculaire, etat fondamental des systemes quantiques confines [H.sup.+.sub.2] et He[H.sup.++]. PACS Nos.: 02.70.Uu, 31.15.-p., 1. Introduction Recently, studies of quantum objects confined by different forms of external potentials have attracted the attention of both physicists and quantum chemists. This is because of the unusual [...]