Strategic alliances have significant impact on Maritime Container Shipping Markets. The vertical and horizontal integration as well as mergers and acquisitions have changed the market dynamics. The MCSM is a strongly integrated market on the supply side. The aim of this paper is to determine, based on empirical data, whether this market is still competitive for its participants, whose are not party of main alliances, and operates services passing across Atlantic and Pacific. For this purpose the Herfindahl-Hirshman Index for members of alliances, namely 2M, THE Alliance and Ocean Alliance, was calculated. The results of computation indicate that the market is moderately concentrated for services passing through Atlantic and still competitive for services passing across Pacific.