Schools whose engineering majors are filled to capacity (which includes many state flagship level schools) need to choose between various methods of admission to the major:
A. Admit directly to the major. For those rejected from the major, but otherwise admissible to the school, some schools admit as undeclared or a second choice major, while other schools reject entirely. However, getting into the major or changing to another “full” major after enrolling can be very difficult, since the only spaces available come from attrition. UT Austin does it this way for engineering. (Note: in California, in most cases, UCs and CSUs do it this way for engineering majors.)
B. Admit to undeclared or pre-major status, then compete for admission to the major after enrolling. This is less certain for those who are sure of their intended major, and can increase the stress and cutthroat competition in one’s first year, since there is concern about being “weeded out”. Admission to the major may be purely by GPA, or it may also include essays. Some schools have an automatic admission to major GPA threshold, below which admission to the major is competitive. Texas A&M does it this way for engineering, with a 3.5 automatic admission to major threshold. Other schools which do it this way include Purdue, Minnesota, Virginia, Virginia Tech, Ohio State. Wisconsin has an odd variant where students are admitted to their majors, but must meet a high GPA requirement (as high as 3.5, depending on the major) to stay in their majors.
C. Combination of A and B. Some students (the top applicants) receive direct admission to the major, but some space in the major is held for competitive admission by enrolled students who are admitted to undeclared or pre-major status. Washington does it this way for at least some majors (notably CS).