  We initiate the study of M-strings in the thermodynamic limit. In this limit
the BPS partition function of M5 branes localizes on configurations with a
large number of strings which leads to a reformulation of the partition
function in terms of a matrix model. We solve this matrix model and obtain its
spectral curve which can be interpreted as the Seiberg-Witten curve associated
to the compactified M5 brane theory.
