In this paper, a Zener-Stroh crack problem in a finite plate is studied. By using the principle of superposition, the original problem is converted into a Zener-Stroh crack problem in an infinite plate and a usual Griffith crack problem in a finite plate. The former problem has a solution in a closed form. The latter problem can he solved by using EEVM (eigen-function expansion variational method). Finally, numerical examples for evaluating the stress intensity factors at crack tips are presented.