Areas that the government is requesting comment from businesses from between now and 16 February include internal workings of companies and partnerships, accounts and returns, rules governing business names and disclosure of company information.
Around 120 regulations, guidance and enforcement processes are to be looked at as part of a campaign launched by the coalition government in April last year.
Business minister Edward Davey said: "We want to have a flexible regulatory framework within company law to allow firms to compete and grow successfully. The Red Tape Challenge is a great way for the public and firms to tell us what is a nuisance or gets in the way of doing business effectively.
"The feedback we receive will allow us to build on the Companies Act 2006, to look at areas such as the audit regime to assist small and medium sized companies as well as the approach to filing documents at Companies House.
"I am open to new ideas to simplify, merge or discard additional rules that will enable firms to do business with more confidence."
The Government has published a discussion paper to coincide with the start of the current sector. It is available at the Red Tape Challenge website.
Roger Barker, head of corporate governance at the Institute of Directors and company law sector champion, said: "We must be sure that regulation is proportionate and that the company law framework protects companies and their creditors, whilst minimising red tape and making the running of a company as simple as possible.
"I look forward to seeing some new and exciting proposals from businesses to help inform this important work."
So far, from over 1,200 regulations considered, the government has agreed to scrap or improve over 50%.