Aims. We use spectral energy distributions (SEDs), Hα line profiles, and visibilities available in the literature to study Achernar's envelope geometry and to propose a possible scenario for its circumstellar disk formation and dissipation. Methods. We use the SIMECA code to investigate possible geometries of the circumstellar environment by comparing our synthetic results with spectroscopic and high angular resolution data from the VLTI/VINCI instrument. We compute three different kinds of models: an equatorial disk, a polar wind, and a disk+wind model. Results. We develop a 2D axial symmetric kinematic model to study the variation of the observed Hα line profiles, which provides clear evidence of Achernar's equatorial disk formation and dissipation between 1991 and 2002. Our model can reproduce the polarwind extension greater than 10 R and a possible equatorial disk (≤5 R ) but we were unable to estimate the wind opening angle. We reproduce the Hα line-profile variations using an outburst scenario, but the disk final contraction requieres an additional physical effect to be taken into account. The polar stellar wind does not appear to be linked to the presence of a disk or a ring around the star. We test the possibility of a binary companion to Achernar, as found by Kervella & Domiciano de Souza (2007, A&A, 474, L49), but conclude that the VLTI/VINCI visibilities cannot be explained by a rotationally-distorted Be star and a companion alone. The presence of a polar jet provides an important component to reproduce the observations even if it is not excluded that the companion could partially influence the observations. New interferometric observations at short baselines (5 ≤ B ≤ 20 m) are mandatory to constrain Achernar's circumstellar envelope, as well as spectroscopic long-term follow-up observational programs to link Achernar's mass-loss episodes with its circumstellar disk formation.