It is running a competition that will share $55,000 (Â£42,000) between the top two people who can make its FUN3D software run up to 10,000 times faster.
The FUN3D code is used to model how air flows around simulated aircraft in a supercomputer.
The software was developed in the 1980s and is written in an older computer programming language called Fortran.
"This is the ultimate 'geek' dream assignment," said Doug Rohn, head of Nasa's transformative aeronautics concepts program that makes heavy use of the FUN3D code.
In a statement, Mr Rohn said the software is used on the agency's Pleiades supercomputer to test early designs of futuristic aircraft.
The software suite tests them using computational fluid dynamics, which make heavy use of complicated mathematical formulae and data structures to see how well the designs work.
Once designs are proved on the supercomputer, scale models are tested in wind tunnels and then finally experimental craft undergo real world testing.
Significant improvements could be gained just by simplifying a heavily used sub-routine so it runs a few milliseconds faster, said Nasa on the webpage describing the competition. If the routine is called millions of times during a simulation this could "significantly" trim testing times, it added.
Nasa said it would provide copies of the code to anyone taking part so they can analyse it, find bottlenecks and suggest modifications that could speed it up. Nasa is looking for the code to run at least 10 times faster but would like it quickened by thousands of times, if possible.
Any changes to FUN3D must not make it less accurate, said Nasa.
The sensitive nature of the code means the competition is only open to US citizens who are over 18.
Nasa is seeking help from coders to speed up the software it uses to design experimental aircraft.