The innovative methods proposed in this thesis provide effective and efficient solutions to the reliability problems of burst and collapse of tubes with random geometric imperfections under internal or external pressure. Steel tubes have broad applications in petroleum offshore engineering and must be designed to a safe but yet economical standard. The variation of imperfections from tube to tube necessitates a statistical characterization in which the burst and collapse pressures become random variables. In order to evaluate the burst and collapse pressure of a pipe with deterministic geometric imperfections, the finite element method is employed with a cylindrical shell element based on classical nonlinear shell theory. This element implements the return mapping algorithm for an elastic/plastic material and includes the effects of shell thinning and geometric imperfections. Incorporation of this finite element program into a reliability program developed for this study provides an effective numerical tool for the probabilistic analyses of the burst and collapse problems. For these analyses, the pipe thickness is modeled as an axially homogeneous and circumferentially inhomogeneous Gaussian random field based on measured data from two groups of pipes. Using the developed shell finite element program, Monte Carlo simulation (MCS) can be applied to the burst/collapse reliability problems. However, the enormous computational effort makes MCS infeasible except as a check for selected cases. Unfortunately, the system reliability method does not apply to the present problems because there are an infinite number of design points due to the special structure of the imperfections. Thus, a new approximate method is developed for the burst problem based on the correlations between the minimum thickness and burst pressure. The probability distribution of minimum thickness is obtained through an innovative homogenization procedure. Similarly, the collapse reliability problem is solved through introduction of a homogenized collapse function whose minimum correlates with the collapse pressure. The proposed reliability methods are applied to selected cases and verified by MCS. The effect of length on reliability in burst and collapse is investigated. Compared to MCS, the efficiency of the new methods makes them especially applicable to engineering problems, such as pipeline design and manufacturing quality control.