Vein fields are fractured domains of the lithosphere that have been infiltrated by hydrothermal fluids, which deposited minerals in response to changing physico-chemical conditions. Because oxygen is a major component of the infiltrating fluid and the surrounding rock matrix, the oxygen isotope composition of minerals found in veins is used to decipher ancient fluid flow within the lithosphere. We use a numerical model to simulate oxygen isotope transport in the Kokanee Range silver-lead-zinc vein field. The model considers advective, dispersive, and reactive transport in a three-dimensional porous rock matrix intersected by high-permeability planes representing fracture zones. Here we show that it is the geometrical configuration of the sources and of the drains of hydrothermal fluids, combined with the fracture pattern, that exerts the main control on the oxygen isotope distribution. Other factors that affect, to a lesser extent, the values and positions of oxygen isopleths are the fluids and rock-matrix isotopic compositions, the isotopic fractionation, the reaction rate constant, and hydraulic conductivities of the rock matrix and fracture zones.