The four include Kiyoshi Takahashi, chairman of Showa, and Takeshi Hemmi, president, who have taken responsibility for the dealings, which led to a loss of 125bn yen (pounds 749m) for Showa.
The resignations were announced as Shell, the world's biggest oil group, reported a 28 per cent surge in net profits to pounds 3.06bn last year, in line with expectations.
Shell's share of the currency speculation is expected to total pounds 196m, of which pounds 131m has been taken with last year's results.
The other two to resign are Yutaka Otaka, managing director, and Yasuyuki Futami, director, both senior executives at Showa's treasury division. Yukihisa Fujita, the treasury manager who is thought to have played a key part in the currency dealings over a four-year period, has been sacked.
Sir Peter Holmes, Shell's chairman, said he had been 'shocked and disappointed' by the currency dealings, which he said were in breach of company policy not to speculate on foreign exchange markets. Shell is sending Neil Gaskell, a senior financial manager at the group, to take over as Showa's finance director.
It appears that the dealings started after one treasury manager tried to recoup losses - amounting to single-figure millions - incurred during the normal course of his job. Although the attempt failed, he continued to expose the company to increasingly large exchange-rate risks.
Shell said the dealings were not discovered earlier because of Japanese accounting practices.
It is understood that the dealings came to light by chance last December during a conversation between a Japanese bank official and a Showa manager.
Shell's profits increase stemmed from higher oil and gas production and the benefits of cost-cutting on virtually unchanged group turnover of pounds 73bn.
Although the group made a pounds 657m provision against higher US retirement and healthcare costs, currency gains rose from pounds 79m to pounds 412m. Underlying net profits, excluding oil stock values, jumped 8 per cent to pounds 3.12bn, thanks to a 92 per cent jump in fourth-quarter profits to pounds 945m.
Net profits from oil exploration and production rose 29 per cent to pounds 1.9bn while the refining and marketing business lifted profits by 7 per cent to pounds 1.2bn. However, overcapacity and weak demand for petrochemicals in Europe pushed the chemicals division from a pounds 23m profit to a pounds 223m loss last year. Capital expenditure fell 9 per cent to pounds 6bn.
The total dividend has been improved by 4.8 per cent to 21.9p. Shell shares closed 3p up at 582p.