The American Bar Association makes all of the merits briefs to the US Supreme court available online.
Don’t rush off to read them if you’re just running your own case in the tribunal. Since the US has a different legal system the law they discuss is irrelevant to you. Also, they argue cases, particularly on appeal, very differently. US appeals are basically decided on the papers. Even in the Supreme Court, lawyers are usually restricted to half an hour oral argument. So US briefs have to argue the whole case, rather than being skeletons to be fleshed out orally.
So, the US briefs aren’t directly relevant and, if you’re just doing the one case, your time is better spent elsewhere.
But, if you do a lot of cases or you’re interested in legal writing, they are well worth a read. Many of the lawyers arguing in the US Supreme Court are brilliant advocates and the US system encourages them to hone their written work. You can learn a lot about how to set out and argue a point by studying their example.
A hat-tip to Carl Gardner, whose Written constitutions: a warning from America prompted this post. And, come to think of it, is also worth reading to see good legal writing.