The asymptotic behavior of the solute velocity and dispersivity for a system of parallel fractures with matrix diffusion is made using numerical modeling and theoretical analyses. The study is limited to linearly sorbing solutes with a constant continuous source boundary condition. Expressions are provided for solute velocity and effective dispersivity in terms of fracture porosity during asymptotic stage using spatial moment analyses. The importance of matrix porosity and fracture porosity on solute velocity as well as the relationship governing effective dispersivity and fracture porosity is discussed for both non-reactive and linearly sorbing solutes. By using a dimensionless effective dispersivity parameter it is shown that the relationship between the fracture porosity and dimensionless effective dispersivity is linear for non-reactive solutes. It is also shown that this holds true for the linearly sorbing solutes with the same proportionality constant. © Springer 2006.