We apply Walborn's Shannon Entropic Entanglement Criterion (SEEC) [S.P. Walborn, B.G. Taketani, A. Salles, F. Toscano, R.L. de Matos Filho, Physical Review Letters 103, 160505 (2009)], to simple harmonic oscillators. In particular, we investigate the entanglement of a system of coupled harmonic oscillators. A simple form of the entanglement criterion in terms of their interaction is found. It is shown that a pair of interacting ground state coupled oscillators are more likely to be entangled for weaker coupling strengths while coupled oscillators in excited states entangle at higher coupling strengths. Interacting oscillators are more likely to be entangled as their interaction increases.