"Samuels and Shillingford were reported at the end of the second day's play on Friday by on-field umpires Richard Kettleborough and Nigel Llong, TV Umpire Vineet Kulkarni and Andy Pycroft of the Emirates Elite Panel of ICC Match Referees," the ICC said in a statement.
"Mr Pycroft handed over the copies of the reports to the West Indies team manager after the conclusion of the Test."
The umpires' reports have cited concerns over the two bowlers' actions, with particular references to Samuels' "quicker deliveries" and Shillingford's "doosras".
"The players are required to submit to an independent analysis of their bowling actions. This analysis must take place within 21 days, and the reports on the independent assessment of their actions must be submitted to the ICC within a further 14 days.
The development comes as a major setback to the team which is already struggling to keep its morale after a shambolic show in the Test series.
"If the players are found to have bowled with an illegal action during the independent analysis then they will be suspended from bowling in international cricket," the ICC stated.