Great circle and rhumb line are the curves on Earth, whose shape is treated as a sphere. Great circle is a part of a large circle and represents the shortest distance between the points. Rhumb line is longer than the great circle, but it crosses every meridian under the same angle, so meanwhile moving, direction change of the moving object is not needed. In the graduation thesis we present the characteristics of the curves and procedures of numerical solving for the situations on individual curves. As a result of the task, we present a program in the MATLAB environment, which, when entering the geographical coordinates of any two places on Earth, calculates the coordinates of places on the great circle and rhumb line, and allows the visualization of results on the Mercator projection map and in Google Earth.