We numerically model the evolution of dust in a protoplanetary disk using a two-phase (gas+dust) Smoothed Particle Hydrodynamics (SPH) code, which is non-self-gravitating and locally isothermal. The code follows the three dimensional distribution of dust in a protoplanetary disk as it interacts with the gas via aerodynamic drag. In this work, we present the evolution of a disk comprising 1% dust by mass in the presence of an embedded planet for two different disk configurations: a small, minimum mass solar nebular (MMSN) disk and a larger, more massive Classical T Tauri star (CTTS) disk. We then vary the grain size and planetary mass to see how they effect the resulting disk structure. We find that gap formation is much more rapid and striking in the dust layer than in the gaseous disk and that a system with a given stellar, disk and planetary mass will have a different appearance depending on the grain size and that such differences will be detectable in the millimetre domain with ALMA. For low mass planets in our MMSN models, a gap can open in the dust disk while not in the gas disk. We also note that dust accumulates at the external edge of the planetary gap and speculate that the presence of a planet in the disk may facilitate the growth of planetesimals in this high density region.