Elizabeth Cross was the daughter of William Cross and Elizabeth Baggly.

Elizabeth was born around 1765.

She was christened on Saturday 21 December 1765.

Elizabeth married Thomas Greenhough on Wednesday 24 September 1794 in Kings Bromley, Staffordshire.

She had the following children from her marriage to Thomas Greenhough:

- Richard Greenhough	born around 1795.
- Francis Greenhough	born around 1798.
- Mary Ann Greenhough	born around 1803.
- Anne Greenhough	born around 1806.
- Ann Greenhough	born around 1810.

Details of Elizabeth's death are not known.