Computational modeling is an important element of systems biology. One of its important applications is modeling complex, dynamical, and biological systems, including viral infections. This type of modeling usually requires close cooperation between biologists and mathematicians. However, such cooperation often faces communication problems because biologists do not have sufficient knowledge to understand mathematical description of the models, and mathematicians do not have sufficient knowledge to define and verify these models. In many areas of systems biology, this problem has already been solved; however, in some of these areas there are still certain problematic aspects. The goal of the presented research was to facilitate this cooperation by designing seminatural formal language for describing viral infection models that will be easy to understand for biologists and easy to use by mathematicians and computer scientists. The ModeLang language was designed in cooperation with biologists and its computer implementation was prepared. Tests proved that it can be successfully used to describe commonly used viral infection models and then to simulate and verify them. As a result, it can make cooperation between biologists and mathematicians modeling viral infections much easier, speeding up computational verification of formulated hypotheses.