Is there a good free software for business process modelling and analysis? What are the different types and how useful are they?

One of the main tasks business analysts are required to engage in is defining the current state of the business. Processes are a key part of the business and should be continually analyzed for bottlenecks or lapses that may have built up over time. In improving the current state, business processes are defined through models. With the right tools in place, you can focus on the task of process modelling with ease 

There are many S/W that can help you but don't know they are free  ,

. Gliffy is a web-based tool for creating diagrams online; no downloads are necessary. It supports UML so whether it's a flowchart or use case diagram you want to draw, Gliffy will deliver. It can also be used to draw interface