Leg-spinner Munday played for Cornwall in the 2001 Cheltenham & Gloucester Trophy before attending Oxford University.
He represented Oxford UCCE in 2003 and 2004 and claimed his maiden five-wicket haul in first-class cricket when he took 5-83 in the 2003 Varsity Match at Fenner’s.
He was called up by England Under-19 in 2004 and played in two of the three Tests as England beat Bangladesh 2-0.
He made his first-class debut for Somerset in August 2005 when he was selected for the county championship match against Essex at Colchester and he took the valuable wicket of Andy Flower in the first innings.
He topped his county's championship bowling averages in 2007 with 14 victims in just three matches. They were taken at 13.71 and included best figures of 8-55.
However, he was not selected for any of the one-day competitions.
In 2008 he struggled to hold down a first-team place and managed only three wickets in three championship outings.
Munday made just one first-team appearance in 2009, in the thrilling championship win at home to Yorkshire, but was awarded a one-year contract that October.