The 66-year-old, from Hackballscross in County Louth, denies failing to furnish tax returns between 1996 and 2004.
The charges arise out of a probe by the Irish police's Criminal Assets Bureau.
The trial is taking place before three judges in a non-jury court and is expected to last three weeks.
Counsel for the state has said that despite Mr Murphy applying for and receiving government grants of more than 100,000 euros (Â£73,600) he did not make any returns to revenue commissioners.
He said he will show that Mr Murphy had access to considerable cash, more than 300,000 euros (Â£220,000), for renting land for silage purposes and for dealing with cattle marts.
Grainne Dalton, a retired official from the Irish Department of Agriculture, conceded under cross-examination that she had not personally seen Mr Murphy or any other grant applicant receive or complete forms.
Mr Murphy's lawyer said his client did not accept that he had played any role in submitting grant applications and denied the signatures on the forms were his hand writing.
The presiding judge agreed to a defence request to delay the trial until Thursday to allow them to access disclosure documents.
If found guilty, Mr Murphy could face up to five years in prison.
The trial of the prominent republican Thomas 'Slab' Murphy at Dublin Special Criminal Court has heard that he had access to considerable cash sums despite not supplying tax returns.