A Study of Paclitaxel With or Without Ramucirumab (LY3009806) in Participants With Gastric or Gastroesophageal Cancer

Inclusion Criteria:

* Have an Eastern Cooperative Oncology Group Performance Status (ECOGPS) of 0 or 1 at study entry.
* Have a histopathologically or cytologically confirmed diagnosis of gastric or gastroesophageal junction (GEJ) adenocarcinoma.
* Have metastatic disease or locally advanced, unresectable disease.
* Have at least 1 measurable lesion based on Response Evaluation Criteria in Solid Tumors (RECIST), Version 1.1.
* Have experienced documented objective radiographic or symptomatic disease progression during first-line therapy, or within 4 months after the last dose of first-line therapy with any platinum/fluoropyrimidine doublet for unresectable or metastatic disease.
* Have adequate organ function.
* Have urinary protein ≤1+ on dipstick or routine urinalysis.

Exclusion Criteria:

* Have undergone major surgery within 28 days prior to randomization.
* Have received any first-line chemotherapy other than platinum and fluoropyrimidine with or without anthracycline for advanced gastric or GEJ adenocarcinoma.
* Have received any previous systemic therapy (including investigational agents) targeting vascular endothelial growth factor (VEGF) or the VEGF receptor signaling pathways.
* Have a history of deep vein thrombosis, pulmonary embolism, or any other significant thromboembolism during the 3 months prior to randomization.
* Have significant bleeding disorders, vasculitis, or had a significant bleeding episode from the gastrointestinal (GI) tract within 3 months prior to study entry.
* Have a history of GI perforation and/or fistulae within 6 months prior to randomization.
* Have experienced any arterial thromboembolic event within 6 months prior to randomization.
* Have uncontrolled arterial hypertension (systolic blood pressure ≥160 millimeters of mercury \[mmHg\] or diastolic blood pressure ≥100 mmHg) despite standard medical management.
* Have a serious or nonhealing wound, peptic ulcer, or bone fracture within 28 days prior to randomization.
* Have a serious illness or medical condition(s).