Fractal dimensions provide an objective means for comparing fractals. They are important because they can be derived from real world data, and they can be measured approximately by means of experiments. Also, they may be viewed as measurement of the shape roughness. In this work, three algorithms for evaluation of fractal dimensions are implemented. These algorithms are based on box counting approach. A comparison is made between the results of these algorithms when evaluating the fractal dimensions of some computer-generated surfaces. These surfaces are of different fractal dimensions. The results showed that the fractal dimension could be used for measuring the shape roughness with an acceptable accuracy. The results showed also that there are significant differences between these methods in accuracy, stability, reliability and the needed time for computation.