We analyze the monic representations of C*-algebras of finite k-graphs. We first introduce $\Lambda$-semibranching function systems of finite k-graphs and associated representations. Then we discuss a specific class of $\Lambda$-semibranching function systems called monic systems, which give rise to monic representations of $C^*(\Lambda)$. The results we discuss in fact completely characterize these representations, generalizing the works of Dutkay-Jorgensen and Bezugli-Jorgensen for Cuntz and Cutnz-Krieger algebras respectively. This is a joint work with Carla Farsi, Elizabeth Gillaspy, Palle Jorgensen and Judith Packer.