It was the 32-year-old's second test with the former champions, who conducted the session in secrecy and gave little away about it.
A spokeswoman said simply that he had "completed another productive day running with the team" in a 2014 specification FW36 car.
There were no timings or details about the number of laps completed.
Kubica's previous test at Silverstone on Oct. 11 was described merely as a 'successful day'.
Williams' British reserve driver Paul di Resta will be in the car on Wednesday at the Hungaroring but the team has said there is no shoot-out between the two for a vacancy that has also yet to be confirmed.
Both are in the frame, however, to replace 36-year-old Felipe Massa should Williams decide not to renew the Brazilian's contract.
Di Resta stood in at short notice to replace the unwell Massa at this year's Hungarian Grand Prix.
Kubica partially severed his right forearm in an horrific 2011 crash during a rally he entered for fun before the start of that Formula One season, and there are lingering doubts about his arm movement.
The fact he has been given two test sessions is a good indication of the level of interest in his performance and potential, however.
Before his accident, Kubica was considered a future world champion with a move to Ferrari in the offing. Former karting rivals Lewis Hamilton and Nico Rosberg, both champions, still hold him in the highest regard.
The Pole also completed 142 laps of the Hungarian Grand Prix circuit in August in a test with Renault that revealed no "obvious roadblocks" to his return, according to the manufacturer.
He is being assisted by Rosberg, the 2016 world champion who started his F1 career with Williams in 2006 before moving to Mercedes.
"He showed in the Renault test he is ready and there's no doubt about that anymore. Physically he is 100 percent in the car," Rosberg told Sky Sports television this month.
(Reporting by Alan Baldwin, editing by Pritha Sarkar)
Share
