We obtain an exact solution of Einstein's equations for a charged, static and spherically symmetric body, surrounded by a fluid of strings and with a cosmological constant. This corresponds to the Reissner-Nordstr\"om (de Sitter)-Anti de Sitter black hole surrounded by a fluid of strings. Some aspects concerning the horizons and geodesic motion are discussed. We also obtain the metric corresponding to the Kerr-Newman black hole surrounded by a fluid of strings, by using a method to construct the rotating solution from its counterpart static one. The horizons, ergoregions, and geodesic motion are analyzed. In both cases, the role played by the fluid of strings was pointed out.