Arguments for the waterfall model

Time spent early on in software production can lead to greater economy later on in the software lifecycle; that is, it has been shown many times that a bug found in the early stages of the production lifecycle (such as requirements specification or design) is cheaper, in terms of money, effort and time, to fix than the same bug found later on in the process. ([McConnell 1996], p. 72, estimates that "a requirements defect that is left undetected until construction or maintenance will cost 50 to 200 times as much to fix as it would have cost to fix at requirements time.") To take an extreme example, if a program design turns out to be impossible to implement, it is easier to fix the design at the design stage than to realize months later, when program components are being integrated, that all the work done so far has to be scrapped because of a broken design.
This is the central idea behind Big Design Up Front (BDUF) and the waterfall model - time spent early on making sure that requirements and design are absolutely correct will save you much time and effort later. Thus, the thinking of those who follow the waterfall process goes, one should make sure that each phase is 100% complete and absolutely correct before proceeding to the next phase of program creation. Program requirements should be set in stone before design is started (otherwise work put into a design based on "incorrect" requirements is wasted); the program's design should be perfect before people begin work on implementing the design (otherwise they are implementing the "wrong" design and their work is wasted), etc.
A further argument for the waterfall model is that it places emphasis on documentation (such as requirements documents and design documents) as well as source code. In less designed and documented methodologies, should team members leave, much knowledge is lost and may be difficult for a project to recover from. Should a fully working design document be present (as is the intent of Big Design Up Front and the waterfall model) new team members or even entirely new teams should be able to familiarize themselves by reading the documents.
As well as the above, some prefer the waterfall model for its simple and arguably more disciplined approach. Rather than what the waterfall adherent sees as "chaos", the waterfall model provides a structured approach; the model itself progresses linearly through discrete, easily understandable and explainable "phases" and is thus easy to understand; it also provides easily markable "milestones" in the development process. It is perhaps for this reason that the waterfall model is used as a beginning example of a development model in many software engineering texts and courses.
It is argued that the waterfall model and Big Design Up Front in general can be suited to software projects which are stable (especially those projects with unchanging requirements, such as with "shrink wrap" software) and where it is possible and likely that designers will be able to fully predict problem areas of the system and produce a correct design before implementation is started. The waterfall model also requires that implementers follow the well made, complete design accurately, ensuring that the integration of the system proceeds smoothly.
Sunil sees the two big advantages of the pure waterfall model as producing a "highly reliable system" and one with a "large growth envelope", but rates it as poor on all other fronts. On the other hand, he views any of several modified waterfall models (described below) as preserving these advantages while also rating as "fair to excellent" on "work[ing] with poorly understood requirements" or "poorly understood architecture" and "provid[ing] management with progress visibility", and rating as "fair" on "manag[ing] risks", being able to "be constrained to a predefined schedule", "allow[ing] for midcourse corrections", and "provid[ing] customer with progress visibility". The only criterion on which he rates a modified waterfall as poor is that it requires sophistication from management and developers. (Rapid Development, 156)