Spinal cord injury (SCI) causes chronic pain in 65% of individuals. Unfortunately, current pain management is inadequate for many SCI patients. Rodent models could help identify how SCI pain develops, explore new treatment strategies, and reveal whether acute post-SCI morphine worsens chronic pain. However, few studies explore or compare SCI-elicited neuropathic pain in rats. Here, we sought to determine how different clinically relevant contusion SCIs in male and female rats affect neuropathic pain, and whether acute morphine worsens later chronic SCI pain. First, female rats received sham surgery, or 150 kDyn or 200 kDyn midline T9 contusion SCI. These rats displayed modest mechanical allodynia and long-lasting thermal hyperalgesia. Next, a 150 kDyn (1 s dwell) midline contusion SCI was performed in male and female rats. Interestingly, males, but not females showed SCI-elicited mechanical allodynia; rats of both sexes had thermal hyperalgesia. In this model, acute morphine treatment had no significant effect on chronic neuropathic pain symptoms. Unilateral SCIs can also elicit neuropathic pain that could be exacerbated by morphine, so male rats received unilateral T13 contusion SCI (100 kDyn). These rats exhibited significant, transient mechanical allodynia, but not thermal hyperalgesia. Acute morphine did not exacerbate chronic pain. Our data show that specific rat contusion SCI models cause neuropathic pain. Further, chronic neuropathic pain elicited by these contusion SCIs was not amplified by our course of early post-trauma morphine. Using clinically relevant rat models of SCI could help identify novel pain management strategies.