The company was established in 1968 in Stavanger by Captain Simon Møkster (1936-1992). Simon Møkster was from the island Møkster, which is located in the Austevoll archipelago, south-west of Bergen. The first vessel he purchased was MV "Mokstein" and this was the start of a 25 years history where Simon Møkster purchased, operated and sold 107 vessels. Sale and purchase was a contributing factor to the continued growth of the company.

Møkster entered the offshore market in 1981 by purchasing and converting the fishing vessel "Strilmøy" into a standby/rescue vessel. "Strilmøy" was at that time the most advanced standby/rescue vessel in operation on the Norwegian continental shelf. Møkster was regarded as one of the pioneers within the standby/rescue segment and became the largest owner and manager of vessels within the standby/rescue segment.

Møkster continued to grow the business within the offshore segment and gradually divested traditional shipping tonnage.

The word ”stril” was in 1975 used for the first time as part of Møkster’s name on a ship. Being from Møkster/Austevoll meant that Simon Møkster was a ”stril” something he regarded as a brand of quality, integrity and hard work. All vessels owned by Simon Møkster Shipping are therefore branded with the name ”stril” as part of the ship-name. Simon Møkster Shipping is today a fully integrated offshore shipping company.

"I like to see the white light from the lighthouse when I work late hours, it gives a feeling of confidence and reminds me of the days as navigator. When in white sector you know that you have enough water under your keel. When in green and red, then you have to change course" – quote from Simon Møkster.