The duo were reported at the end of the second day of West Indies innings and 126-run defeat to India in the second Test, which finished in Mumbai on Saturday.
A report from all four match officials highlighted specific concern with Shillingford's 'doosra' and Samuels' 'quicker ball'.
Both players have 21 days to undertake an independent analysis of their bowling actions, with a report then due to be sent to the International Cricket Council within a further 14 days.
Shillingford and Samuel have been through the process to prove their bowling actions before.
Samuels was reported in February 2008 and resumed bowling in international cricket in September 2011 while Shillingford - who claimed 11 wickets in India's two innings during the short series - was reported in November 2010 before returning to bowl in June 2011.
The ICC confirmed both players would be available for the upcoming three-match one-day international series against India, with unless they elect to undergo the analysis of their action instead.
The spin duo could, however, be called for no-ball by standing umpires who deem their actions are illegal.
"Until the independent assessments are received, the players shall be permitted to continue bowling in international cricket," a statement read.
"At any time throughout this period the players are subject to being called on the field by the umpire(s) in accordance with Law 24.2 and the consequences of such Law must apply.
"During this period a further match officials' report will, however, have no consequence."