@acer thanks for the response.

>Have you tried the command kernelopts(numcpus=40) or used some other values? How does that affect the performance?

Yes, this was my first thought, however changing numcpus to 40 didn't make any difference.

>How much benefit (if any) do you see from your current use of Threads:-Seq over using just seq?

The speed-up is dramatic.  I checked time[real], and computation time goes down by a factor of at least 1/2 but sometimes much more. I was hoping to get another speed-up by utilizing more threads, but as you say, perhaps I'm already at the limit for this particular machine.

The complicated procdure is entirely symbolic, basically a large amount of polynomial arithmetic. Each call to this function might take minutes to hours to compute. It is (or at least should be) thread safe.

Now I'm wondering if something like 

Grid:-Seq([Threads:-Seq( f(i,j), j=1..N)], i=1..N)])

would produce the expected result and utilize the resources better.

Thanks for the advice!