Mary Smythe was born about 1536, of Stainforth, Hatfield, West Riding, Yorkshire, England and died about 1567.  

• Parents: daughter of "Elder" William Smythe ( d. between 25 Jan 1559 and 2 May 1560) & Agnes Simkinson

Married

1. about 1553 in Stainforth, Hatfield Near Doncaster, Yorkshire, England to John Simkinson, who died on 23 Dec 1562.
2.  on 1 Jan 1565 to William Brewster II, son of William Brewster and Maude Mann, (William Brewster II was born in 1535 in Scrooby, Nottinghamshire, England and died on 10 Aug 1608 in Scrooby, Nottinghamshire, England.). She was his first wife; he married Prudence Perkins second abt 1567.

Children of John Simkinson & Mary:

1. Thomas Simkinson4 b. 1555?, d. 1611
2. Dorothy Simkinson4 b. 1557?, d. after 1591

Children of William Brewster and Mary:

1. William Brewster (abt  1566 - 1644), the Mayflower Passenger, married Mary ---, who came in The Mayflower, with her husband. He is possibly the only noted son of William & his first wife Mary Smythe Brewster (NEHGR 125:150) as suggested by various documents at Doncaster, Yorkshire, England and other research.

Sources

•  Hunt, John G. "The Mother of Elder William Brewster of the Mayflower", in The New England Historical and Genealogical Register. (Boston: New England Historic Genealogical Society), Vol. 124:250, 1970 . 
• Their son William was named along with his half-brother Thomas Simkinson as nephew in the will of their uncle John Smythe of Hull in 1592, which comprehensively named his nieces and nephews. The fact that she was not mentioned in the will suggests that she had no further children after William, and thus probably died soon after 1566. Mary, as wife of John Simkinson, was named in the will of her father William Smythe. 
• An undated proceeding found in the Great Britain Public Record Office, rev. C2 Eliz. B 31/1 reports "Bill of Complaint by William Bruester and Mary his wife, the late wife of John Symkinson late of Doncaster, Yorks. The said John was seized of lands in Doncaster and in his lifetie did convey them to the said Mary then his wife for the term of her life and afterwards he died at Doncaster."

Links

•  http://www.mayflowerfamilies.com/mayflower/william1_brewster_family.htm
•  http://www.geneajourney.com/brwstr.html
•  http://myfamilyhistoryjj.com/TNG/getperson.php?personID=I35678&tree=1
•  http://www.jackandpatt.com/freeman/p623.htm#i12454