How to simulate elastic material with restoring shape I'd like to simulate a rubber-like material. This material if deformed would experience a restoring force to its original shape, a bit like a school rubber ereaser. 

I tried with a spring-mass system but the system become quickly instable, moreover it's computational expansive.

Doing some research I found out I could simulate this behaviour through finite element method If I understood well. The problem is I haven't got the right mathematical tools to understand this method.

So how would you face up to this problem?
Resources, links, tutorials, papers are welcome.
A good introduction to finite element methods for deformable body animation is Sifakis and Barbič's course FEM Simulation of 3D Deformable Solids from SIGGRAPH 2012.

However, since you say


  I tried with a spring-mass system but the system become quickly instable, moreover it's computational expansive.


you should know that a finite element model is usually more expensive than a mass-spring system. If you're having problems with instability, you should try keeping your mass-spring system but (i) reducing the time step, or (ii) doing implicit integration; see the "Implicit Methods" chapter of the Witkin and Baraff notes.

You can also consider position-based dynamics or projective dynamics, which are fast, stable, and easier to implement than FEM. They may be good enough for your needs, unless you require high accuracy or nonlinear material models.