The Shulhan Aruch (264:6) writes that one fulfills the Misva of Shabbat candle lighting on the level of Misva Min Ha’mubhar (the highest standard of Misva observance) by using specifically olive oil. While other oils and substances are acceptable for the Misva, the most preferable manner of fulfilling this obligation is by using olive oil. In fact, the Sefer Hasidim (by Rabbi Yehuda HaHasid of Regensburg, Germany, late 12th century), in Siman 272, tells of a certain Jew who lived an exceptionally long life, and no source of merit could be found to explain his longevity, other than the fact that he always ensured to light the Shabbat candles with olive oil. It is also written in the Siddur of the Arizal (Rav Yishak Luria of Safed, 1534-1572) that there is profound Kabbalistic significance to lighting the Shabbat candles with olive oil. And the Hid"a (Rav Haim Yosef David Azulai, 1724-1807), in his work Mahazik Beracha, writes that if olive oil is available, one must make a point of using it for the Shabbat candles. He further notes the Gemara’s comment that one who properly fulfills the Misva of Shabbat candles is rewarded with children who are Torah scholars, and he writes that one should therefore ensure to observe this Misva on the highest standard, with olive oil, to which Torah scholars are compared.
(It is told that the wives of some great Torah Sages did not use olive oil for the Shabbat candles; the wife of the Steipler Gaon (Rav Yaakov Yisrael Kanievsky, 1899-1985), for example, used wax candles. Nevertheless, we follow the view of the Shulhan Aruch and the Hid"a, that it is preferable to use olive oil.)
If one week a woman sees that she does not have olive oil, what should she use for lighting the Shabbat candles?
The Mishna Berura (Rav Yisrael Meir Kagan of Radin, 1839-1933) writes that one who does not have olive oil should, in principle, use other high quality oils that produce a clear, steady flame, and these oils are preferable to wax candles. However, wax candles in modern times are made in a manner that produces a clear, steady flame, and their quality is thus no lower than that of fine oils. Therefore, since wax candles produce a clear, steady flame as is appropriate for the Misva, and there is no concern that one might tilt the candles to improve the flame, wax candles are just as suitable for the Misva as other oils, such as canola or cottonseed oil. This applies to paraffin candles, as well. Thus, one should endeavor to use olive oil for the Misva, but if olive oil is not available, one may use wax or paraffin candles.
This applies as well to a woman who normally uses olive oil for the Shabbat candles but one Shabbat goes away to a place where olive oil is not available. The woman in this case may certainly use wax or paraffin candles. When she committed to use specifically olive oil, she had in mind the lighting in her home, understanding from the outset that when she goes away for Shabbat she may not necessarily have access to olive oil.
Summary: It is preferable to use olive oil for the Shabbat candle lighting. If olive oil is not available, one may use wax or paraffin candles, or other oils such as canola and cottonseed oil which produce a clear, steady flame.