Outbreak of avian influenza within a poultry farm is studied mathematically. A system of two nonlinear ordinary differential equations is introduced as a model. Unknown variables of these differential equations are populations of susceptible birds and infected birds. Analysis of the model shows that the most effective measure against outbreak of avian influenza within a poultry farm is a constant removal of infected birds, and that removal of infected birds can solely prevent an outbreak. The analysis also shows that vaccination is effective in conjunction with removal of infected birds, and that vaccination can not prevent an outbreak without the removal of infected birds.