Influenza has been responsible for human suffering and economic burden worldwide. Isolation is one of the most effective means to control the disease spread. In this work, we incorporate isolation into a two-strain model of influenza. We find that whether strains of influenza die out or coexist, or only one of them persists, it depends on the basic reproductive number of each influenza strain, cross-immunity between strains, and isolation rate. We propose criteria that may be useful for controlling influenza. Furthermore, we investigate how effective isolation is by considering the host's mean age at infection and the invasion rate of a novel strain. Our results suggest that isolation may help to extend the host's mean age at infection and reduce the invasion rate of a new strain. When there is a delay in isolation, we show that it may lead to more serious outbreaks as compared to no delay.