The money would then stay in the envelopes until the time came to pay the corresponding bill, at which point the funds would be taken out and used. The major problem with this method, of course, is that it was designed for a time when most transactions were handled in cash. People received pay envelopes containing bills and coins, and the folding green stuff exchanged hands for most purchases and payments. In today's world of checks, credit cards, and electronic banking, such a system is a nightmare. You would spend an enormous amount of time making cash withdrawals and deposits.
Safety is another concern.
Even worse is the fact that money sitting around in envelopes isn't working for you. Instead of just laying there, gathering dust, you want those funds out there making more money. All of these decisions are carefully documented on paper. That done, the list is carefully filed away, and the family goes out and begins their spending. The problem here is there is no easy way to enforce the budget plan.