The classifications given by railroads to their steam locomotive fleets were as varied as the machines themselves with several different designations within a particular class! Frisco steam locomotives were likewise distinguished by a wide range of numerical classes (the SLSF was one of few railroads of its day to distinguish its steam types by numbers rather than letters). In any event, the information here is most certainly not a complete, all-time listing of the Frisco's steam fleet and also is merely meant to list the general types of steam locomotives operated by the railroad.
The St. Louis-San Francisco Railway, commonly known as simply the Frisco has a storied history of two halves. During the railroad’s first 60 years it had a very interesting and tumultuous history going through a number of name changes and bankruptcies (resulting in so many names). However, after its final name as the St. Louis-San Francisco, the railroad did quite well and prospered for its last 60+ years of operation before becoming part of the large Burlington Northern system in the very early 1980s.
While the St. Louis-San Francisco Railway was a regional Class I in nature it did operate some large steam locomotives including 4-8-4 Northerns, 4-8-2 Mountains, and 2-8-2 Mikados. Today, sevearal Frisco steam locomotives survive preserved (nearly two dozen!) and displayed although a few are currently undergoing some type of restoration.
Class 337, 354, 359, 361
These classes included Frisco's fleet of 2-6-0 Moguls.
Class 742
The Frisco's Class 742 included its fleet of 4-6-0 Ten-Wheelers.
For more reading about steam locomotives like those operated by the Frisco consider Perfecting the American Steam Locomotive by author J. Parker Lamb. As the name implies the book details the earliest history of steam engine technology, even before it was used in railroad applications. His book later explores the development of steam locomotive technology in the United States from the 19th through the 20th centuries, covering not only the most popular steam locomotive designs but also the most successful manufactures to build them. The book has received excellent reviews and is a great resource on steam locomotives and a fine reference tool; you should find it very useful.
Also, consider the book American Steam Locomotives from author Brian Solomon. While this publication does not include quite as much technical data as Lamb's book, Perfecting the American Steam Locomotive, it is still a very good resource with lots of information and best of all, is loaded with photographs! If you're interested in perhaps purchasing either (or both) of these books please visit the links below which will take you to ordering information through Amazon.com, the trusted online shopping network.