The transport of chemical species in groundwater systems is of interest to a variety of earth scientists. Development of transport models that incorporate phenomena which govern the partitioning of chemical species between aqueous and solid phases is fundamental to understand processes such as ore deposition, chemical diagenesis of sediments and migration of toxic chemicals. A large number of chemical transport models, of varying degrees of complexity, have been devised in the past. However, none of these models considers explicitly the fractured character of three dimensional geological systems. Incorporation of discrete fractures in a model will provide an adequate representation of the aquifer. We present FRAC3DBC which is a numerical model for mass transport with biochemical and chemical reactions in a 3D discrete fractured media. While porous media is defined in 3D, the fractures are represented by 2D planes. Bacteria growth, substrate consumption and release of metabolic products are considered. Also taken in consideration are equilibrium and kinetic chemical reactions. A sequential iterative procedure is used to solve the coupled physical and chemical transport equations. We present here solutions for simplified problems that show some of the characteristics of the model. Reactive transport in a one-dimensional column with a unit cross section is simulated in two stages. In the first stage the system initially contains 2 aqueous species A and B and one solid species AB. At time greater than zero, an incoming fluid containing aqueous species A, C and D in known concentrations enters the upstream boundary. The incoming fluid dissolves the solid AB and the dissolution front is monitored. In the second stage, for the same system we consider a possible complexation of C and B to form BC. Using finally the same chemical and physical system, we incorporate discrete fractures to investigate their effect on reactive transport. These tests demonstrate the applicability of the model and the influence of fratures on reactive transport.