In this paper, we present an overview of all analytical engineering solutions delivered over the past 60 years for corrosion problems in pressure vessels. We briefly detail the strengths and weaknesses of existing approaches, thus demonstrating the need for novel uniform corrosion analysis methods for both current and new applications. To complement the review, we also present a new analytical model allowing the estimation of the lifetime of pressured elastic vessels with mechanically assisted corrosion. Both internal/external pressure and internal/external corrosion are captured, and dissolution-driven corrosion is also considered. The readily implemented method improves existing analytical approaches and is shown to be effective for thin and thick shells, as well as various loading and corrosion intensity and geometrical conditions.