This chapter covers the failure modes and mechanisms of concern in hydroprocessing reactor vessels and the methods used to assess lifetime and performance. It begins with a review of the materials used in the construction of pressure-vessel shells, the challenges they face, and the factors that determine shell integrity. The discussion addresses key properties and design parameters including allowable stress, fracture toughness, the effect of microstructure and composition on embrittlement, high-temperature creep, and subcritical crack growth. The chapter also provides information on the factors that affect cladding integrity and ends with a section on life-assessment techniques.