The possibility of explaining the collected data for the hot Jupiter WASP-12b using a model with a stationary, quasi-closed, aspherical envelope around the exoplanet is considered. The influence of variations of the parameters of the stellar wind on the size and shape of the quasi-closed envelope is considered, and the maximum size of the envelope is determined to be Δφ ≃ 0.17 (φ is the orbital phase of the planet measured from the position of the main minimum). In order for the UV eclipse to begin at the phase indicated by observations with the Hubble Space Telescope, φ ≃ 0.83, the size of the envelope must be Δφ ≃ 0.12, or 21Rpl (Rpl is the radius of the planet). This size is in very good agreement with theoretical estimates obtained assuming solar parameters for the stellar wind. Unfortunately, this conclusion is not firm, since the available observations begin at phase φ ≃ 0.83, hindering any conclusions about the character of the light curve at earlier phases. In the case of a quasi-closed or an open envelope, the UV eclipse could begin at earlier phases, φ ≃ 0.78 and φ ≃ 0.7, respectively. Determining the true nature of the envelope of WASP-12b will require additional UV observations beginning from a phase earlier than the phase corresponding to the eclipse of a quasi-closed envelope of the maximum size,φ < 0.78.