It is shown that very simple iteration routines for solving a very broad class of transcendental equations, including many of great importance in physical applications, can be developed and used quite conveniently with pocket calculators such as the Hewlett−Packard HP−35 and others of similar capability. Questions of convergence and methods of extending domains of convergence are discussed. While the methods considered are not new to mathematicians and computer scientists, it does not seem to be generally appreciated that they may be so easily and systematically used with machines of this class. While it is true that some repetitive key punching is required, this is not usually very tedious; the solution of most equations is accomplished with the ease (and within the time span) of typing a three or four line paragraph on a typewriter, once the routine is developed. Some of the procedures considered can also be used for the solution of systems of simultaneous transcendental equations. The methods which are used are extremely convenient and practical when a few or even a few dozen transcendental equations are to be solved. If there are a few hundred, however, it is probably best to use the IBM 360!