The Planck Sunyaev-Zeldovich Cluster catalogue provides an all-sky set of SZ detected galaxy clusters, which is the first of its kind. SZ signals are independent of redshift which allows a greater volume of space to be surveyed, compared to luminosity dependent X-ray and optical surveys. The statistical analysis of strong gravitational lensing from a complete and well defined set selection provides an opportunity for studying the largest structure in the universe and addresses issues raised in previous lensing cluster analysis. Previous cluster statistics have shown an overabundance of arc detections relative to cosmological theory, which may be due to biases in cluster detection methods. Optical cluster surveys do not probe deep enough, X-ray surveys are biased towards less dense and massive cluster profiles, and both suffer from a lack of a statistically significant sample set. The two year Planck mission has produced a large SZ selected cluster set, from which 147 clusters with signal-to-noise ratios > 6.0 and redshifts ranging from 0.14 < z > 1.8, are analyzed for detections of strongly lensed arcs. 72 lensing clusters with 214 total arcs were analyzed for comparison to theory and previous arc catalogues in terms of Einstein radii, arc orientations, length to width ratios, magnitudes, surface brightnesses, and arc frequency.