Motivation: LTR retrotransposons are mobile elements that are able, like retroviruses, to copy and move inside eukaryotic genomes. In the present work, we propose a branching model for studying the propagation of LTR retrotransposons in these genomes. This model allows us to take into account both the positions and the degradation level of LTR retrotransposons copies. In our model, the duplication rate is also allowed to vary with the degradation level. Results: Various functions have been implemented in order to simulate their spread and visualization tools are proposed. Based on these simulation tools, we have developed a first method to evaluate the parameters of this propagation model. We applied this method to the study of the spread of the transposable elements ROO, GYPSY and DM412 on a chromosome of Drosophila melanogaster. Availability and Implementation: Our proposal has been implemented using Python software. Source code is freely available on the web at https://github.com/SergeMOULIN/retrotransposons-spread.