In permanent breast seed implant brachytherapy, radioactive palladium-103 seeds are implanted into the breast to treat early-stage breast cancer. Despite promising outcomes, adoption of this technique is limited by the resources and expertise required. Clinically, treatment planning requires manual optimization, and specialized skills. This thesis endeavours to improve this process by investigating the impact of delivery uncertainties on dosimetry and providing recommendations for constructing PBSI treatment plans that are robust to uncertainty. We developed a Monte Carlo algorithm to simulate PBSI delivery uncertainty. Using this simulator, we quantified the impact of random and systematic needle placement uncertainty for three idealized spherical clinical target volumes (CTVs) of varied volume. At clinically anticipated levels of uncertainty, introducing systematic errors less than 10 mm results in changes to target coverage of less than 5%, indicating that the planning target volume (PTV) margin is sufficient to account for systematic errors. Additionally, we present expressions that can be used to estimate the expected coverage based on a given institutional seed placement uncertainty. The simulation algorithm was used to produce 3000 simulated post-implant dose volume histograms for 109 patients who had received PBSI at one of two treatment centres. The simulated target coverage was used to quantify the robustness of each treatment plan. We analyzed correlations between planned PTV and ETV (evaluation target volume) DVH indices, and the simulated ETV coverage. The planned ETV D90% was found to exhibit the strongest correlations to median target coverage leading us to recommend that the ETV D90% be assessed at treatment planning. Correlations between geometric characteristics related to the implant volume, and simulated target coverage were assessed, finding that smaller ETV volumes exhibited more variability in simulated target coverage. A strong correlation was observed between the mean ETV-PTV margin and simulated target coverage. For 90% probability of delivering at least 90% of the prescription dose to at least 90% of the target volume, a planned ETV D90% of 124 Gy and a mean ETV-PTV margin of at least 6 mm are recommended.