Common Software
SolidWorks
SolidWorks is one of the most common design software in the modern age of engineering. One simply cannot mention 3D CAD software or stress analysis without mentioning the behemoth that is SolidWorks. Conveniently, with an Experimental Aircraft Association (EAA) membership, one can get a discounted rate for the non-commercial version of this groundbreaking software suite.
XFoil
XFoil is "an interactive program for the design and analysis of subsonic isolated airfoils". Produced by MIT, XFoil assists in the design and selection of airfoils for aircraft of any size.
OpenVOGEL
OpenVOGEL is a completely free (even ads) aeromechanical design software. The simulation is capable of being run on a laptop or desktop, and is capable of analyzing steady aerodynamics, rigid body dynamics (unsteady flight simulation), and aeroelasticity (also known as flutter).