Some past epidemics of different influenza subtypes (particularly A/H3N2) in the US saw co-circulation of vaccine-type and variant strains. There is evidence that natural infection with one influenza subtype offers short-term protection against infection with another influenza subtype (henceforth, cross-immunity). This suggests that such cross-immunity for strains within a subtype is expected to be strong. Therefore, while vaccination effective against one strain may reduce transmission of that strain, this may also lead to a reduction of the vaccine-type strain's ability to suppress spread of a variant strain. It remains unclear what the joint effect of vaccination and cross-immunity is for co-circulating influenza strains within a subtype, and what is the potential benefit of a bivalent vaccine that protects against both strains. We simulated co-circulation of vaccine-type and variant strains under a variety of scenarios. In each scenario, we considered the case when the vaccine efficacy against the variant strain is lower than the efficacy against the vaccine-type strain (monovalent vaccine), as well the case when vaccine is equally efficacious against both strains (bivalent vaccine). Administration of a bivalent vaccine results in a significant reduction in the overall incidence of infection compared to administration of a monovalent vaccine, even with lower coverage by the bivalent vaccine. Additionally, we found that with greater cross-immunity, increasing coverage levels for the monovalent vaccine becomes less beneficial, while introducing the bivalent vaccine becomes more beneficial. Our work exhibits the limitations of influenza vaccines that have low efficacy against non-vaccine strains, and demonstrates the benefits of vaccines that offer good protection against multiple influenza strains. The results elucidate the need for guarding against the potential co-circulation of non-vaccine strains for an influenza subtype, at least during select seasons, possibly through inclusion of multiple strains within a subtype (particularly A/H3N2) in a vaccine.