Computer Aided Engineering (CAE) Finite Element Analysis (FEA) Types
There are many different types of analysis which can be undertaken, each yielding a degree of information depending on the problem in hand. We start simple and then add complexity only if required.
Linear Statics 
The backbone of most FEA. Linear Statics is now well known and trusted. It's a great designer's tool since it puts you in 'the zone' for getting designs about right straight from the off. Linear refers to material, geometric and boundary condition properties that can be sovled - i.e materials in their elastic state and obey Hooke's Law where stress is driectly related to strain or vice versa. Young's modulus and Poisson's Ratio are required to solve. Static refers to a loading condition which does not change with time. Most problems or representative models can be solved using this method.
Linear Dynamic
Dynamic analysis can also be termed as Response Analysis. This evaluates the model over time to a given or known excitation of the system. The input may have varying loads over time. Used when a better understanding of transient loading characteristics occur. Again, the material, geometric and boundary properties are linear.
Modal Analysis
Natural frequencies and harmonics given by the stiffness of a system. Modal analysis is used so that phenomenon such as resonance is avoided - if you know the natural frequencies of a system, then you can change the natural frequnices by changing/varying the design, change the design so that the interactions are different (such as adding damping), or change the way the system/components are to be used.
Frequency Reponse
Vibration. Very important for analysis of rotating machinery/equipment such as car rotors, fans/turbines etc. This gives the forced response of a system to a known excitation in terms of freqeuncies and harmonics generated. Crucical for avoiding resonance or constructive/destructive waves. Follows on from Modal Analysis.