Mathworks: Matlab
 Popular and comprehensive mathematical analysis package

Mathsoft: Mathcad
 Easy to use mathematical spreadsheet program

Insightful: S-Plus
 Widely used statistical analysis software

R Statistical  Computing
Powerful open source statistical analysis program.

Wolfram Research: Mathematica
Maths analysis software

Palisade
Risk analysis software

BrainMaker
Neural network software. Back prop networks with GA optimiser.

Solver.com
Excel and SDK solver. Implements Sharpe, Markowitz portfolio optimisation.

Tradestation 2000
Industry standard back-testing package

TradersStudio
Back testing software with portfolio testing capability.

Trading Recipes
Multi-market portfolio testing software

Seer Trading
Portfolio back testing software.

Tradestation Research Group
Provide a range of software add-ons to the Tradestation platform

Inside Edge Systems
Provides portfolio analysis and add on software products for Tradestation.