This work aims to study some methods for mitigating the increase in pressure in confined annuli (APB - Annular Pressure Build-up) of oil wells. Throughout the life of the well, various operations provoke temperature variations, leading to pressure increases and decrease in the annular spaces. In some cases, the pressure variations can result in casing failures. Ultradeep waters wells present even more extreme temperature and pressure conditions, consequently raising the APB levels observed. In this context, mitigation techniques appear as alternatives to ensure the integrity of the well, keeping APB levels within the allowed limits. The methodology adopted to achieve the objective of this work is divided into four macro steps: i) study on the APB, identifying the theoretical aspects. At this stage, the study of the APB simulator, developed by Vasconcelos (2019), is also carried out, which is used in this work to model the phenomenon. Including comparing the results, for a reference scenario, with those achieved through the software StrinGnosis®, widely used by the oil and gas industry; ii) study of the methods for mitigating APB, understanding the functioning of each technique. At this stage, the open shoe or cement shortfall, rupture disks, and compressible foam methods are selected for more advanced studies based on their advantages; iii) implementation of computational routines in the simulator to reproduce the behavior of APB with the presence of each of the three previously selected techniques; and iv) final evaluation of the methods’ ability to mitigate the issues related to APB. Based on the results, the APB simulator presents a maximum difference of 3.66% compared to StrinGnosis®. Regarding the studied mitigation methods, in the scenario considering fluid drainage to the formation, different rock permeabilities cause variations of up to 1000 psi in the studied model. Furthermore, increasing the drainage section is not effective beyond a certain depth. With the use of rupture disks, less resistant casings associated with the installation of disks can be economically advantageous, maintaining the integrity of the well. With the use of synthetic foams, it is possible to evaluate their length and positioning in the annuli to keep the APB within the allowed limits. In this context, the present work contributes to studies on annular pressure build-up (APB) in oil wells and APB mitigation techniques. Additionally, it assesses, in a simplified manner, the integrity of well casings subjected to APB loads.