To interpret positron annihilation data in solids in terms of the electron momentum density and electron charge distribution, both the electron-positron interaction and positron wave function have to be considered explicitly. In the present work we discuss the effect of the shape of the positron wave function on the calculated positron annihilation rates in a variety of solids, for different types of electrons (core, s, p, d, f). We show that the form of the positron distribution in the Wigner-Seitz cell has a crucial effect on the resulting core electron contribution to the positron annihilation characteristics. The same is observed for the localised d and f electrons in transition metals Finally we study the influence of the positron wave function on the electron-positron momentum density in elemental Si.