Almost 40% of young Americans were living with their parents, siblings or other relatives in 2015, the largest percentage since 1940, according to an analysis of census data by real estate tracker Trulia.

Despite a rebounding economy and recent job growth, the share of those between the ages of 18 and 34 doubling up with parents or other family members has been rising since 2005. Back then, before the start of the last recession, roughly one out of three were living with family.

The...