Joyce describes a modern journey, not by keeping his characters Stephen, Bloom, Molly, Haines and Mulligan at the backdrop of myth but by putting his characters in moulds of mythological characters. Joyce's protagonist Bloom is exiled in his own country Ireland. He is in deep anguish. The untimely death of his infant son produced a piercing wound in his heart. His being ostracized, made him isolated. His being cuckolded by his wife Molly humiliated him to the core. He is afflicted with the modern malaise like alienation, isolation, exile- consciousness and disintegration of his self. Bloom is on a journey to live an assertive life. Bloom is on the look out for the wholeness of his self. This journey of alienated and exiled modern Irish hero Leopold Bloom is given a mythic dimension. To dramatize the journey of Leapold Bloom Joyce does not evoke a mythic parallel. Rather Joyce treats Leopold Bloom as a modern Ulysses shipwrecked in his marital life. Exactly like shipwrecked Ulysses of Homer, Joyce’ Ulysses Leopold Bloom is shipwrecked in his marital life. Just as the Homeric hero Odysseus's wife Penelope was surrounded, Bloom's wife Molly was also paid constant courtship by Boylan. Just a Homeric Ulysses was in exile during his ten years journey on the sea, Joyce modern Ulysses Leopold Bloom feels lost and ignored on the soil of Dublin. There is evoked no parallel between Homeric Ulysses and the modern Ulysses like Leopold Bloom. Joyce did not draw parallels rather James Joyce endeavored to represent. Leopold Bloom as modern Ulysses whose sufferings are no less heroic than that of the Homeric hero Ulysses.
In Ulysses James Joyce presented Stephen Dedalus as a young Irish artist who is languishing in the lap of heavy debt, loss of self respect, poverty, neglect, isolation, alienation and the hopeless climate of Dublin. Stephen Dedalus is capable of being an artist. But his father does not understand the gravity of his aspirations. Stephen is disappointed by this shallow understanding of his father. He is shocked awfully and remorseful pain at the death of rising to artistry Stephen Dedalus became hopeless and frustrated. As his frustration deepened Stephen sidetracked. He began to deviate from the norm of creative aspiration. With desire inspiration for further creative pursuits Stephen was all the time on the look out for a father figure. In his search for father figure James Joyce treated Stephen not a modern hero close to Telemachus in Homer Ulyssess. According to Joyce, Stephen is not like Homeric Telemachus, rather he is modern Telemachus. Just as Homer's Telemachus came out to search for his father so that he could know how worthwhile his life is, Joyce's Stephen comes out in the Irish world in search for a father figure who could inspire him to the highest level of creative pursuits. In narrating the modern journey of Stephen and Leopold Bloom, James Joyce made not an instrumental but a constructive use of myth. Joyce cites myth, not as a device, but at the end of the modern narrativization.
In Ulyssess James Joyce sought to establish Molly as modern Penelope. Like Penelope in Homer's Odyssey Molly was paid courtship by Boylan. Molly's growing attraction towards Boylan humiliated Leopold Bloom. Bloom was helpless to take action against Molly's growing adulterous relationship with Boylan. But like Homeric Ulysses Bloom saw one possibility of stopping his wife Molly's adulterous affinity in Boylan. After Bloom got a glimpse of son figure in Stephen, he felt somewhat awakened. With this level of awakening and redemption Leopold Bloom developed as assertive will. Throughout his life in past Bloom has been servile to his wife. That is why Molly dominated him. He always used to bring breakfast to Molly in her bed. This servility on the part of Bloom had reduced her status as a masculine being. Once he developed his assertive will he was in a position to exert his say over her. In this way Joyce has portrayed Molly as modern Penelope.
Joyce describes a modern journey by presenting modern characters not as replies of mythic heroes, heroines, but as figures as equal as mythic characters.