Apple is claiming that more than a quarter of Samsung's $30.4 billion (£19.3 billion) tablet and mobile phones sales in the US are a result of infringing its patents.
The American conglomerate is demanding up to $2.75 billion of damages from its South Korean rival. This figure includes an estimate of profits lost to infringing gadgets.
However Samsung's lawyers have argued that Apple does not have sufficient evidence to merit such an award of damages as their high-profile court case entered its third week.
This is the latest in a long line of claims against Samsung in the trial, with one of the American technology giant's key witnesses Susan Kare calling Samsung's devices "confusingly similar" to that of Apple's.
Earlier this year, Apple failed in a similar trial in the UK after the judge claimed that Samsung's products couldn't have infringed patents as they weren't as cool.
It is expected that this case will last for around three months in the US and could be a landmark ruling either way.
Posted by Samantha Green