Try Like Below
C# code:
string xml =@"<detail><err:Errors xmlns:err=""http://www.zzzz.com/XMLSchema/XOLTWS/Error/v1.1""><err:ErrorDetail><err:Severity>Hard</err:Severity><err:PrimaryErrorCode><err:Code>9120203</err:Code><err:Description>Missing or invalid Address.</err:Description></err:PrimaryErrorCode></err:ErrorDetail></err:Errors></detail>";
var element =XElement.Parse(xml);
string Severity =element.Descendants().FirstOrDefault(e => e.Name.LocalName =="Severity" ).Value;
string Code =element.Descendants().FirstOrDefault(e => e.Name.LocalName =="Code" ).Value;
string Description =element.Descendants().FirstOrDefault(e => e.Name.LocalName =="Description" ).Value;
VB code
Dim xml As String = "<detail><err:Errors xmlns:err=""http://www.zzzz.com/XMLSchema/XOLTWS/Error/v1.1""><err:ErrorDetail><err:Severity>Hard</err:Severity><err:PrimaryErrorCode><err:Code>9120203</err:Code><err:Description>Missing or invalid Address.</err:Description></err:PrimaryErrorCode></err:ErrorDetail></err:Errors></detail>"
Dim element = XElement.Parse(xml)
Dim Severity As String = element.Descendants().FirstOrDefault(Function(e) e.Name.LocalName = "Severity").Value
Dim Code As String = element.Descendants().FirstOrDefault(Function(e) e.Name.LocalName = "Code").Value
Dim Description As String = element.Descendants().FirstOrDefault(Function(e) e.Name.LocalName = "Description").Value