Study of Weekly Paclitaxel With Ramucirumab in Participants With Advanced Gastric Adenocarcinomas

Inclusion Criteria:

* Has a histopathologically or cytologically confirmed diagnosis of gastric or gastroesophageal junction (GEJ) adenocarcinoma
* Has an advanced or metastatic solid gastric adenocarcinoma that has failed standard therapy
* Has resolution of all clinically significant toxic effects of prior therapy, surgery, treatment with an investigational agent or device, treatment monoclonal antibody or small molecule, and radiotherapy or chemotherapy.
* Has adequate organ function
* Eligible participants of reproductive potential (both sexes) agree to use adequate contraceptive methods (hormonal or barrier methods) during the study period and for 12 weeks after the last dose of study medication

Exclusion Criteria:

* Has undergone major surgery within 28 days prior to the study, or subcutaneous venous access device placement within 7 days prior to the study registration date
* Has elective or planned surgery to be conducted during the trial
* Has had treatment with an investigational agent or device, an antineoplastic small molecule, or antineoplastic radiotherapy or chemotherapy
* Was previously treated with a chemotherapy regimen containing nitrosoureas or mitomycin C
* Has had treatment with an antineoplastic monoclonal antibody within 8 weeks prior to the study registration date
* Has a history of deep vein thrombosis, pulmonary embolism, or any other significant thromboembolism prior to the study registration date
* Has experienced any arterial thrombotic event, including myocardial infarction, cerebrovascular accident, or transient ischemic attack, within 6 months prior to the study date
* Is receiving therapeutic anticoagulation with warfarin, low-molecular weight heparin or similar agents. (Participants receiving prophylactic, low-dose anticoagulation therapy are eligible provided that the coagulation parameters International Normalized Ratio (INR) ≤ 1.5, prothrombin time (PT) and partial thromboplastin time (PTT) or - Is receiving chronic therapy with nonsteroidal anti-inflammatory agents \[Aspirin use at doses up to 325 milligrams/day (mg/day) is permitted\]
* Has significant bleeding disorders, vasculitis, history of postoperative bleeding complications, hemoptysis or had a significant bleeding episode from the gastrointestinal (GI) tract within 3 months prior to the study date
* Has a history of GI perforation and/or fistulae within 6 months prior to the study date
* Has symptomatic congestive heart failure, unstable angina pectoris, or symptomatic or poorly controlled cardiac arrhythmia
* Has uncontrolled arterial hypertension despite standard medical management.
* Has a serious or nonhealing wound or peptic ulcer or bone fracture within 28 days prior to the study date
* Has a bowel obstruction, history or presence of inflammatory enteropathy or extensive intestinal resection, Crohn's disease, ulcerative colitis, or chronic diarrhea
* Has a serious illness or medical condition(s)
* Is pregnant or lactating
* Has received treatment with another investigational drug or participation in another interventional clinical trial within 28 days prior to the study date