The UK corrugated case manufacturer, which is part of €600m (£484m) Belgian group VPK, said it was necessary to fill the position following a "tough" period for the business.
"When Paul died suddenly in the early New Year, we were obviously all left devastated," said Rigid Containers managing director Richard Coward.
He added: "While it was understandably tough on many people, business had to continue, so we quickly recruited the services of an interim, to ensure the smooth running of the financial side of our business.
"We used this time to recruit a full-time replacement to Paul. I am delighted to welcome Lars to the team and look forward to working with him for the years ahead."
Maynard, who has held senior board positions across a range of industries, said he will play his part in helping the Desborough and Selby-based business grow.
He said: "It is obviously very hard to replace someone who was so well-liked and respected.
"But I look forward to the challenges of assisting the management team in taking Rigid forward as our business continues to grow, both in volume and profitability."
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