L-systems are widely used in the modelling of branching structures and the growth process of biological objects such as plants, nerves and airways in lungs. The derivation of such L-system models involves a lot of hard mental work and time-consuming manual procedures. A method based on genetic algorithms for automating the derivation of L-systems is presented here. The method involves representation of branching structure, translation of L-systems to axial tree architectures, comparison of branching structure and the application of genetic algorithms. Branching structures are represented as axial trees and positional information is considered as an important attribute along with length and angle in the database configuration of branches. An algorithm is proposed for automatic L-system translation that compares randomly generated branching structures with the target structure. Edit distance, which is proposed as a measure of dissimilarity between rooted trees, is extended for the comparison of structures represented in axial trees and positional information is involved in the local cost function. Conventional genetic algorithms and repair mechanics are employed in the search for L-system models having the best fit to observational data.