This text grew out of notes for a course taught to graduate students in physical oceanography at the College of Oceanic and Atmospheric Sciences at Oregon State University. The students are typically in their second year of graduate school, having passed introductory courses in theoretical physical oceanography. This is the background assumed for the course. Most of the students at this point have seen some numerical analysis. The course, and hence this text, is intended for all students of physical oceanography. Major emphasis is on those features that distinguish models of the ocean from other models in computational fluid mechanics. The intent is to examine ocean models critically, and determine what they do well and what they do poorly. We will ask when we can be confident that the model reflects nature, and when we can say that it is likely that we are looking at a feature of the model itself.