The Flying Phantom capsized in thick fog while towing a cargo vessel on the River Clyde near Glasgow.
Captain Stephen Humphreys, 33, and Eric Blackley, 57, both from Gourock, Inverclyde, died along with Bob Cameron, 65, from Houston, Renfrewshire.
Clydeport Operations Limited was charged with breaching health and safety laws following the incident.
The company, based at Robertson Street, Glasgow, will go on trial at the High Court in Edinburgh on September 22.
The case is expected to last up to eight weeks.
Clydeport denies failing to identify adequately the risks associated with towing in a particular stretch of the Clyde Harbour Area during darkness and fog and provide pilots with the relevant information and training.
The company also denies failing to ensure an efficient weather forecast and monitoring system was in place.
The sinking occurred six days before Christmas when the Flying Phantom ran aground and was overtaken by cargo boat the Red Jasmine, which pulled the tug over on its side.
A fourth crewman, Brian Aitchison, 37, from Coldingham in the Borders, managed to swim free and cling to a buoy and was rescued.