  A theoretical framework for the calculation of shear and bulk viscosities of
hadronic matter at finite temperature is presented. The framework is based on
the quasi-particle picture. It allows for an arbitrary number of hadron species
with point-like interactions, and allows for both elastic and inelastic
collisions. Detailed balance is ensured. The particles have temperature
dependent masses arising from mean field or potential effects, which maintains
self-consistency between the equation of state and the transport coefficients.
As an example, we calculate the shear and bulk viscosity in the linear $\sigma$
model. The ratio of shear viscosity to entropy density shows a minimum in the
vicinity of a rapid crossover transition, while the ratio of bulk viscosity to
entropy density shows a maximum.
