Printed board circuits tracing program design need in testing steps. In case of preplanarization stage it is need to use planar graph data for test set. This paper presents a simple algorithm for generating a family of random planar graphs based on a triangulated graph that can be used in algorithms on graphs. The algorithm is based on the principle of removing random edges and generate both an adjacency matrix and a flat graph drawing. Generated graphs are connected undirected graphs without loops and multiple edges, without bridges and articulation points, without vertices with a local degree less than or equal to two. Results of performance measurement experiments are given.