Estimating the maximum stress in a rock mass based on hydraulic fracturing data typically depends on identification of the breakdown and/or secondary breakdown ("reopening") pressure. Errors in this estimate can be attributed to injection system compressibility, coupled viscous fluid flowin the hydraulic fracture, and crack growth through the varying stress field surrounding a wellbore. The role of these mechanisms has not been well-quantified. Here, a coupled numerical model that includes the compressibility of the injection system and the flow of a viscous fluid in a plane-strain hydraulic fracture extending from a wellbore in the presence of a non-isotropic in situ stress field provides a basic tool for estimating the order of the error associated with analysis of the breakdown pressure under non-ideal conditions. The result is model-based guidelines on the values of relevant dimensionless parameter groups to ensure sufficient accuracy, and when these guidelines cannot be met under field conditions, the model can be further applied to obtain first order corrections that account for compressibility, viscosity, and near-wellbore effects.